Stack played as a goalkeeper for Arsenal, Beveren, Millwall, Reading, Leeds United, Wolverhampton Wanderers, Plymouth Argyle, Blackpool, Hibernian, Barnet, Kerala Blasters and Eastleigh.

Stack was on the bench as Arsenal clinched the 2003–04 FA Premier League title at White Hart Lane on 25 April 2004.

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.

On 24 July 2009, Stack agreed a two-year deal with Scottish Premier League club Hibernian.

Stack established himself as Hibs' first choice goalkeeper during the early part of the 2009–10 season, but then suffered recurring back problems.

[15] 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.

[17] 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.

[27] 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.

[31][32] 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.

[34] After the conclusion of the 2016 ISL season, Stack returned to England to sign for National League side Eastleigh.

[35] On 7 April 2018, Stack was involved in an injury time equalising goal (which was credited to Ryan Cresswell) in a National League game against Wrexham.

In December 2019, Stack acted as caretaker assistant manager to Hayden Mullins following the sacking of Quique Sánchez Flores.