He made his Bundesliga debut in dramatic fashion on 25 February 2007 against league leaders Schalke 04. With starting goalkeeper Hans-Jörg Butt serving a suspension, Adler saved ten shots on goal, repelling Schalke's repeated attacks. A breakaway goal by Stefan Kießling in the 85th minute gave Leverkusen a 1–0 upset victory. Leverkusen manager Michael Skibbe praised Adler's "world-class saves". His strengths are his quick reactions. He stopped Schalke's record of 13 games unbeaten, Stuttgart's record of five games unbeaten and Hamburg's four-game winning spree with a saved penalty kick against Rafael van der Vaart. Since then, Adler became a first choice goalkeeper until newly signed Bernd Leno took his place due to injuries. Adler announced that he was set to leave the club as his contract expired at the end of the 2011–12 season and on 17 May 2012 he joined Hamburger SV for a free transfer after twelve years with Leverkusen.
Adler has been a club captain at all levels of competition and at the German Under-19 championships he was one of the star players of the tournament.
Adler has made four appearances for the German U-21 team under the leadership of Dieter Eilts. He was part of the German team that finished as runners-up in Euro 2008. After the retirement of Jens Lehmann and death of Robert Enke, he became first choice during the World Cup qualifying. He made his debut for Germany on 11 October 2008 in a World Cup qualifier against Russia. Despite having been confirmed as Germany's main team goalkeeper for the World Cup, a serious rib injury prevented him from travelling to South Africa. He was out of contention for the national team for two years, but was recalled in November 2012 for a friendly against the Netherlands after putting in impressive performances since joining Hamburger SV. However, since the injury and in view of the World Cup in Brazil he is second choice keeper behind Manuel Neuer.