In 1985 Bridges turned to the dark side as the psychopath in "Jagged Edge" trying to con then kill Glenn Close (sadly for filmgoers everywhere he failed in the latter attempt). He played Lawrence Block's Matt Scudder in 8 Million Ways to Die, a film that should have/could have been great - Andy Garcia and Roseanne Arquette co-star and it was directed by the great Hal Ashby - but I think I'm right in saying Ashby was dying so the film is (understandably) all over the place. He fared better in a tight little thriller, "The Morning After" (1986), although it was really a vehicle for Jane Fonda, who was riding high at the time. His slack-jawed serial killer in the unnecessary re-make of the Dutch film "The Vanishing" (1993) is best passed over and "Blown Away" (1994) suffers from an over-the-top Tommy Lee Jones performance as an unhinged bomber. "Arlington Road" (1999) though is a neat thriller with Bridges up against a creepy Tim Robbins.
A year earlier, of course, he had defined the hippy slacker as The Dude in "The Big Lebowski", the weirdest crime film you'll ever see. He himself looks pretty weird bald as the villain in "Iron Man" (2008) but is back with the pony tail in "The Men Who Stare At Goats (2009).
Then there's the path less travelled - the films he might have been in had he not turned them down. It's well known he was a contender to play Travis Bickle in Taxi Driver and turned down Indiana Jones. But he was also considered for Don Johnson's part in "Miami Vice", Nick Nolte's part in "48 Hours", Michael Douglas's part in "Fatal Attraction" [told you he should have killed Glenn Close in "Jagged Edge"], Martin Sheen's part in "Apocalypse Now", Bruce Willis's part in "Twelve Monkeys" and the part of John Rambo in "First Blood".
Keanu Reeves's part in "Speed" was actually written with Bridges in mind and he and Nick Nolte were contenders for good guy/bad guy in Michael Mann's "Heat". Back in 1988 he and Nolte were cast in "Tequila Sunrise" but Nolte dropped out so Jeff did too. (Mel Gibson and Kurt Russell took the parts.)
In short: The Dude Abideth.