Banks was born in Sheffield, West Riding of Yorkshire, and brought up in the working-class area of Tinsley. The family later moved to the village of Catcliffe after his father set up a (then-illegal) betting shop. This brought greater prosperity but also misery; one day Banks's disabled brother was mugged for the shop's daily takings, and died of his injuries some weeks later. Banks left school in December 1952 and took up employment as a bagger with a local coal merchant, which helped to build up his upper body strength. He spent a season playing for amateur side Millspaugh F.C. after their regular goalkeeper failed to turn up for a match; the club's trainer spotted Banks amongst the spectators and invited him to play in goal as he was aware that Banks had previously played for Sheffield Schoolboys. His performances there earned him a game in the for Rawmarsh Welfare, however a 12–2 defeat to Stocksbridge Works on his debut was followed by a 3–1 home defeat, and he was dropped by Rawmarsh and returned to Millspaugh. Still aged 15, he then switched jobs to become a hod carrier.
He was scouted by Chesterfield whilst playing for Millspaugh, and offered a six-game trial in the youth team in March 1953. He impressed enough in these games to be offered a part-time £3-a-week contract by manager Teddy Davison in July 1953. The reserve team were placed in the Central League on account of a powerful club director rather than on merit, and Banks conceded 122 goals in the 1954–55 season as the "Spireites" finished in last place with only three victories. Banks was posted to Germany with the Royal Signals on national service, and won the Rhine Cup with his regimental team. He recovered from a fractured elbow to help the Chesterfield youth team to the 1956 final of the FA Youth Cup. There they were beaten 4–3 on aggregate by Manchester United's famous "Busby Babes" – a team that included both Wilf McGuinness and Bobby Charlton.
Banks was given his first team debut by manager Doug Livingstone, at the expense of long-serving Ron Powell, in a game against Colchester United at Saltergate in November 1958. The game ended 2–2, and Banks kept his place against Norwich City in the following match; by the end of the season he had missed only three games, those owing to injury. With no goalkeeping coaching to speak of, Banks had to learn from his mistakes on the pitch, and he soon developed into a modern vocal goalkeeper who ordered the players in front of him into a more effective defence. Having just 23 league and three cup appearances to his name, it came as a surprise to Banks when Matt Gillies, manager of club Leicester City, bought him from Chesterfield for £7,000 in July 1959; this also meant a wage increase to £15 a week.
Banks faced competition from five other goalkeepers, including 30-year-old Scotland international John Anderson and 25-year-old Dave MacLaren. He started the season as the reserve team's goalkeeper. This in effect made him the club's second choice, ahead of four of his rivals but behind first team choice MacLaren. He had played four reserve team games when MacLaren picked up an injury, and manager Matt Gillies selected Banks for his Leicester debut against Blackpool at Filbert Street on 9 September. The match finished 1–1, with Jackie Mudie's strike cancelling out Ken Leek's opener. Banks retained his place for the 2–0 loss to Newcastle United at St James' Park three days later. With McLaren fit again, Banks was sent back to the reserves but, after the first team conceded 14 goals in the next five games, he was recalled and became the first-choice goalkeeper for the remainder of the season. The defensive record did not improve at first, with Banks conceding six in a heavy defeat by Everton at Goodison Park, but he improved in each match and the Foxes settled for a comfortable 12th-place finish. In training, he worked extensively on improving his weaknesses, such as coming for crosses. He put in extra hours during training and came up with practice sessions to improve his skills – this was largely unique in an era where there were no specialized goalkeeping coaches. In the summer, both Anderson and MacLaren departed, leaving Banks as the club's undisputed number one ahead of a group of understudies.
Leicester finished sixth in , and managed to beat champions Tottenham Hotspur at White Hart Lane. Yet their greatest accomplishment was in reaching the final of the FA Cup, with Banks conceding only five goals in their nine games en route to the final, and keeping three clean sheets in the semi-final and two replays against Sheffield United. Goals from and Ken Leek finally broke the deadlock in the second replay at St Andrew's. Their opponents in the final at Wembley were Tottenham, who had already won the First Division title by an eight-point margin. Right-back Len Chalmers picked up a severe injury early in the match, and with Ken Leek dropped for disciplinary reasons in favour of rookie Hughie McIlmoyle, City were effectively playing with ten men and offered little threat going forward. and Terry Dyson gave Spurs a 2–0 win and the first "" of the 20th century, with Banks unable to prevent either goal.
The season proved to be highly disappointing, as Leicester finished 14th in the league and exited the FA Cup at the hands of Stoke City. The only highlight was the club's participation in the European Cup Winners' Cup, which actually put Banks in the difficult position of choosing to play for his club against Spanish club Atlético Madrid or choosing to attend the England versus match as a non-playing squad member. He elected to attend both games, leaving London at full-time to reach Leicester 30 minutes before the kick-off against Madrid. A last-minute goal earned the Spaniards a 1–1 draw at Filbert Street. In the return leg, Banks saved an Enrique Collar penalty, but Atlético were awarded a second penalty which Collar converted, and Leicester lost the game 2–0 (losing the tie 3–1 on aggregate).
Banks broke his nose at Craven Cottage on the opening day of the 1962–63 season, in a 2–1 defeat by Fulham. Leicester went to chase a possible double, reaching the FA Cup semi-finals whilst lying top of the table in April. City beat Liverpool 1–0 at Hillsborough to reach the final, with Banks keeping a clean sheet despite his goal being under a near-constant siege from the Merseyside club. The News of the World reported that Liverpool had had 34 attempts on goal to Leicester's one, and Banks later stated that it was his finest performance at club level. Unluckily, Banks then broke a finger in a 2–1 defeat by West Bromwich Albion at The Hawthorns, and was out injured as Leicester lost their final three league games, ending the season in a disappointing fourth place. In the 1963 FA Cup Final Banks and the rest of the team underperformed, and lost the game 3–1 to Manchester United.
City ended the season in 11th place, having been inconsistent all season. Success instead came through the , as they beat West Ham United 6–3 over two legs in the semi-finals to reach the final against Stoke City. The opening tie at the Victoria Ground finished 1–1 in extremely muddy conditions as Banks spilled a shot from Bill Asprey, with Keith Bebbington pouncing on the rebound. Back at Filbert Street, goals from Mike Stringfellow, and won the game for Leicester 3–2 and settled the tie at 4–3.
Banks started the season on wages of £40 a week, and the club only agreed to pay £60 a week in December. These miserly wages made it difficult for the club to spend the £80,000 it received from the sale of Frank McLintock – he had put in a transfer request over dissatisfaction with his pay and quality replacements were reluctant to join a club that paid full internationals like Banks and McLintock no more than the base rate that rival clubs paid to average players. Leicester finished 18th in the league and were knocked out of the FA Cup by Liverpool at Anfield in the sixth round. In the League Cup, City struggled to get past Peterborough United (in a replay), Grimsby Town and Crystal Palace (in a replay), before they recorded an 8–1 victory over Coventry City at Highfield Road. After easing past Plymouth Argyle in the semi-finals, Banks found himself playing in another . However Chelsea won the final after successfully defending their 3–2 win at Stamford Bridge with a goalless draw at Filbert Street.
Banks missed the first nine games of the season after breaking his wrist when diving at the feet of Northampton Town's Joe Kiernan in a pre-season friendly. Leicester finished the season in seventh spot, and exited both cup competitions at the hands of Manchester City.
Despite being a World Cup winner in the previous summer, Banks was dropped towards the end of the season in favour of highly promising teenage reserve Peter Shilton. Manager Matt Gillies was blunt, telling Banks "we [Gillies and the club's directors] think your best days are behind you, and you should move on". Teammate Richie Norman told Banks that Gillies was pressured into the decision, Shilton having told the board he would leave the club unless he was given first team football. Banks was transfer listed at £50,000, the same price the club received for Derek Dougan in March 1967. However, many of the big clubs were unwilling to spend such a sum on a goalkeeper. Liverpool manager Bill Shankly showed strong interest, but could not convince the club's board of directors to agree to such a large fee for a goalkeeper. West Ham United manager Ron Greenwood was prepared to match the fee, but instead signed Kilmarnock's for £65,000 because he had already agreed terms with Kilmarnock and did not want to go back on his word. Terms were instead agreed with Stoke City, a mid-table First Division side.
"I've not come here to retire you know. I've come to here to win something."
— Banks speaking upon signing with the club after critics questioned Waddington's policy of signing veteran players.
On leaving Filbert Street, Banks requested a loyalty bonus from Leicester, and was told by Matt Gillies "We've decided not to pay you a penny. There's to be no compensation payment and that's final." Banks then refused the move until Stoke boss Tony Waddington seemingly negotiated a £2,000 payment out of Leicester. It was only some years later that Banks was informed that Stoke had actually made the payment, not Leicester. Waddington valued good goalkeepers highly, and the two built up a close relationship. During this time, Banks moved to Madeley, Staffordshire. He replaced as the club's number one, and kept goal in the last four games of the 1966–67 season, making his home debut at the Victoria Ground in a 3–1 win over his former club Leicester.
Banks fitted in well at Stoke, as Waddington built a team of veteran players who were judged by some to be past their best. The Potters struggled near the foot of the First Division table in the 1967–68 and 1968–69 campaigns, before rising to ninth place in the 1969–70 season. Banks remained a reliable stopper for the club, though on 1 March 1969 he was knocked unconscious at Roker Park by Sunderland's Malcolm Moore, and his replacement conceded four goals in a 4–1 defeat. Banks also played a season for the Cleveland Stokers of the American United Soccer Association in the summer of 1968: he played seven of the short-lived club's 12 games in Cleveland, Ohio.
Banks made what he believed to be three of the best saves of his career in a Stoke shirt. In the first instance he saved and caught a powerful and well-placed header from Manchester City's Wyn Davies from just eight yards out; in the second case he saved a Francis Lee header at Maine Road; and he made his third great save for the club by catching a volley from Tottenham Hotspur's Alan Gilzean that had been hit from just six yards out at White Hart Lane.
Stoke began to compete for honours in the 1970–71 season, though despite impressive victories against the top two clubs – Arsenal and Leeds United – City ended the season in mid-table obscurity. The club's great achievement was in reaching the semi-finals of the FA Cup, beating Millwall, Huddersfield Town, Ipswich Town and Hull City en route. Facing Arsenal at Hillsborough in the semi-finals, they lost a two-goal lead to draw 2–2, and were then beaten 2–0 in the replay at Villa Park.
Despite another mid-table finish in 1971–72, Stoke beat Chesterfield, Tranmere Rovers, Hull City and Manchester United to reach another FA Cup semi-final. They again faced Arsenal, and once more a draw at Hillsborough meant a replay at Goodison Park. The Gunners' goals in a 2–1 victory came from a disputed Frank McLintock penalty and a goal that television replays showed was clearly offside. In a May 2011 interview, Banks said that he still felt "cheated" out of a chance to play for the club in an FA Cup final. Stoke and Banks found solace in the League Cup, though it took them 11 matches to reach the final after overcoming Southport, then Oxford United in a replay, Manchester United in a second replay, Bristol Rovers, and then West Ham United in a second replay following an aggregate draw after two legs. In extra-time of the second leg with West Ham, Banks fouled Harry Redknapp, conceding a penalty, and then saved Geoff Hurst's powerful spot-kick to keep City in the competition. They then faced Chelsea in at Wembley. Peter Osgood beat Banks with a hooked shot just before half-time, but goals from Terry Conroy and George Eastham won Stoke the game 2–1. At the end of the season Banks was named as the , becoming the first goalkeeper to receive the honour since Bert Trautmann in 1956.
On 22 October 1972, while driving home from a session of work on his injured shoulder with the Stoke physiotherapist, Banks lost control of his new Ford Consul (a re-badged Ford Granada Mk 1) car, which ended up in a ditch. He had attempted to overtake a car on a sharp bend and collided with an oncoming Austin A60 van. He was taken to the North Staffordshire Hospital and during an operation received 200 stitches in his face and over 100 micro-stitches inside the socket of his right eye, and was told the chances of saving the sight in his eye were 50–50. His sight never returned, and as the loss of binocular vision severely limited his abilities as a goalkeeper, he retired from professional football the following summer.
Fort Lauderdale Strikers
In April 1977 he went to play as a named superstar in the North American Soccer League (NASL) for Fort Lauderdale Strikers. The Strikers won their division in 1977, and Banks was named NASL Goalkeeper of the Year after he conceded only 29 goals in 26 games – the best defensive record in the NASL. He also played one League of Ireland game for St Patrick's Athletic, keeping a clean sheet in a 1–0 win over Shamrock Rovers at on 2 October 1977. He returned to Fort Lauderdale and played 11 games in the 1978 season.