Since Caddyshack, Murray has made consistently good work with a comedic edge and an increasing depth of sadness and aggression. Rushmore brought it to the surface, but it's always been there. So you look and look hard, Oscar, and you try and say anybody else is more deserving.
The Man Who Knew Too Little (1997)--This film had the misfortune of being a spy comedy in the year of Austin Powers. Everybody was too busy with annoying British catchphrases to appreciate Murray's understated role as the ignorant, foolish hero in the footsteps of The Pink Panther's Inspector Clouseau. Murray demonstrates the rare ability of an actor to make even the most far-fetched ideas seem totally plausible.
Mad Dog and Glory (1993)--Though this was not the best film, Murray went to toe-to-toe with Robert De Niro (breaking the Goodfella's nose in the process) and it worked. Assuming he was too goofy to be evil in Scrooged, this was Murray's first truly villainous character. That endearing yet intimidating quality served him well later in Kingpin, Wild Things and Rushmore.
The Royal Tenenbaums (2001)--Rushmore was a public rebirth for Murray, but his decision to take a lesser role in Wes Anderson's third film spoke to a creative desire for growth and complexity, not just top billing. His small, quiet and pitiable role as the bushy-bearded academic almost stole the show from Gene Hackman.
Hamlet (2000)--You can't say this one didn't raise an eyebrow. He's gonna do Shakespeare? Damn right. Murray gave the role of Polonius some serious meat, playing a stern but concerned parent and total nervous kiss-ass at the same time.
Groundhog Day (1993)--The real miracle of this movie was that it was so good. The outrageous premise should have failed miserably, but thanks to Murray's performance (and some smart editing) we all saw a person truly change his ways, and we were touched by it.