I'm sure every film buff out there has a favourite Val Kilmer movie, but mine is his first film - Top Secret! (1984), the ridiculous comedy film in which he portrayed the Elvis-like singing sensation Nick Rivers, who journeys behind the Iron Curtain and gets involved in a spy plot that is very much like the 1944 movie the Conspirators. As Kilmer himself noted, being that he was a young actor, it was a huge challenge to take on such a wacky comedy role; Kilmer succeeded because he portrayed Nick earnestly, a straight man in a very, very wacky movie.
But I'm sure most film buffs are going to point to Tombstone (1993). And yes, even I - a man who does not especially like westerns - point to Kilmer's performance as Doc Holliday as a terrific piece of acting. Perhaps Tombstone is the western movie for people who don't like westerns? Anyway, go watch Tombstone if you haven't already.
Obviously, there's much more I could mention; I have one friend who loves the Ghost and the Darkness (1996); my sister loved Willow (1988); my wife really likes the Saint (1997).
Rest in peace, Mr. Kilmer.