Stack joined Arsenal in summer 1998, and signed his first professional contract in July 2000. The 2002–03 season saw Stack loaned out to Belgian club Beveren, along with three other Arsenal players. In December 2002, Stack came under physical attack during a Beveren match, as hooligans charged at him. He punched one of the hooligans in the face, and riot police were quickly on the scene. His Arsenal debut came in a League Cup match against Rotherham on 28 October 2003, a match his team won 9–8 on penalties; Stack scored in the shootout. He played in all of Arsenal's five matches in the competition, losing in the semi-finals to Middlesbrough. Stack was on the bench as Arsenal clinched the 2003–04 FA Premier League title at White Hart Lane on 25 April 2004. Stack was loaned to Millwall for the entirety of the 2004–05 season. On his return, he was loaned to Reading, at the start of the 2005–06 season.
Reading
Stack joined Reading permanently on 30 December 2005, on a two-and-a-half-year contract. During the 2005–06 season, he made four appearances in the League Cup and three in the FA Cup. On 27 October 2006, Stack signed a three-month loan deal with Championship side Leeds United, whose manager Dennis Wise had previously signed Stack for Millwall. The loan deal was extended to the end of the 2006–07 season on 29 January 2007. Stack competed for the starting position with Neil Sullivan, Tony Warner and Casper Ankergren at various points of the season, but Leeds were relegated at the end of the season. Shortly after returning to Reading, Stack was signed on a one-month loan by Wolverhampton Wanderers, following an injury to their first-choice goalkeeper Matt Murray. His loan spell was later extended to January 2008, and then again to the end of the 2007–08 season. Stack was released by Reading, following their relegation from the Premier League, on 16 May 2008.
Plymouth Argyle
Stack signed a two-year contract with Championship club Plymouth Argyle in July 2008, after training with the club. He made his competitive debut for Argyle on 9 August 2008, with a start against former loan club Wolves. On 27 November 2008, Stack made Blackpool the sixth loan club of his career. However, a month later he returned to Plymouth without making an appearance for the Seasiders. He was loaned to Wolverhampton Wanderers for a second time towards the end of the season. Plymouth released Stack from his contract with the club with effect from 1 August 2009.
Hibernian
On 24 July 2009, Stack agreed a two-year deal with Scottish Premier League club Hibernian. He made his debut in the Scottish League Cup second round win against Brechin, and retained his place for the following league match against Celtic. Stack established himself as Hibs' first choice goalkeeper during the early part of the 2009–10 season, but then suffered recurring back problems. Stack returned to the Hibs starting line up on 20 February in a 1–0 defeat against Motherwell, but was again sidelined when he suffered an eye injury in April. He made just one league appearance in the early part of the 2010–11 season, partly due to a recurrence of the back injury. Stack regained his place in the Hibs team in February 2011, as new manager Colin Calderwood decided to give opportunities to each of his goalkeepers under a rotation policy. Soon afterwards, however, Stack suffered a shoulder injury that required surgery. Despite that setback, Stack agreed a new one-year contract with Hibs during May 2011. Stack played regularly during the 2011–12 season, but suffered a thigh injury during the Scottish Cup semi-final that caused him to miss the last five league games and the 2012 Scottish Cup Final. Stack left Hibernian at the end of his contract in May 2012.
Barnet
Stack had trials with Preston North End and Watford in the 2012–13 pre-season. On 23 August 2012 he signed for League Two club Barnet. He was sent off in a 2–1 defeat against Fleetwood Town on 29 September. He was eventually handed the captaincy in the absence of both Edgar Davids and Barry Fuller. After a string of excellent performances, in January 2013, he was given a three-year contract extension until June 2016. He saved a 94th minute penalty in the last ever game at Underhill Stadium, a 1–0 win against Wycombe Wanderers on 20 April 2013. Stack started the game against Northampton in the final game of the season, which they went on to lose 2–0, thus relegating Barnet to the Conference. In the 2013–14 season, Stack became team captain after Edgar Davids' resignation. Stack won promotion with the Bees by winning the Conference title of 2014–15 with the bees. He lost his place to Jamie Stephens in the 2015–16 season, and left the club in July 2016 despite being offered a new deal.
Kerala Blasters
Stack joined Kerala Blasters in a joint player/goalkeeping coach role in August 2016.
Eastleigh
After the conclusion of the 2016 ISL season, Stack returned to England to sign for National League side Eastleigh. On 7 April 2018, Stack was involved in an injury time equalising goal in a National League game against Wrexham. Stack left Eastleigh in September 2018 to take a coaching position with Watford.
