I mostly enjoy action movies, but also enjoy comedies and dramas. Here's a list of my favorites, sorted alphabetically by genre. 

Action

Broken Arrow (1996)
Rated R
Starring: John Travolta, Christian Slater
Director: John Woo

Travolta is excellent playing the evil villain. The plot's a little thin, but solid action and great special effects make it worth seeing.

Enemy of the State (1998)
Rated R
Starring: Will Smith, Gene Hackman
Director: Tony Scott

Probably the best Will Smith movie to date, he plays a more serious role than is typical for him. This is a suspenseful drama/action movie with plenty of spy gadgets and political intrigue.

Eraser (1996)
Rated R
Starring: Arnold Schwarzenegger
Director: Chuck Russell

Typical Schwarzenegger which means pretty lame acting (but he is getting better), plenty of action, and just enough humor thrown in. 

The Long Kiss Goodnight (1996)
Rated R
Starring: Geena Davis, Samuel Jackson
Director: Renny Harlin

The acting is a little weak, but non-stop action and a few good one-liners make it worthwhile. Davis plays one tough woman. 

The Rock (1996)
Rated R
Starring: Nicholas Cage, Sean Connery
Director: Michael Bay

Suspenseful with plenty of action. Cage and Connery are both great as unlikely heroes. 

Tomorrow Never Dies (1997)
Rated PG-13
Starring: Pierce Brosnan, Jonathan Pryce
Director: Roger Spottiswoode, Desmond Llewelyn

An improvement over Goldeneye, particularly the opening scene. Some absolutely great car and motorcycle scenes. Although, as usual for 007, a very hokey plot. Worth seeing if you like action, though.

True Lies (1994)
Rated R
Starring: Arnold Schwarzenegger, Tom Arnold
Director:

A highly entertaining action-comedy that's a basic rip-off of James Bond style movies but takes itself less seriously. 

U.S. Marshals (1998)
Rated R
Starring: Tommy Lee Jones, Wesley Snipes
Director: Stuart Baird

Sequel to The Fugitive, at least for the federal marshals. Much more action, but a less sophisticated plot. 

Action/Sci-Fi

The Fifth Element (1997)
Rated PG13
Bruce Willis, Milla Jovovich
Director:

An eclectic movie that I enjoyed a lot more in my home than in the theater. Great special effects and a lot of humorous scenes. Excellent demo movie but a little weak in the bass.

The Matrix (1999)
Rated R
Starting: Keanu Reeves, Laurence Fishburne
Director: Larry Wachowski, Andy Wachowski

One of the best movies I've seen in years. Original plot with non-stop action that will keep you on the edge of your seat from beginning to end. So what if Keanu Reeves can't act, this movie is loads of fun.

Terminator 2 - Judgment Day (1991)
Rated R
Starring: Arnold Schwarzenegger
Director: James Cameron

A classic Schwarzenegger action movie. If you haven't seen this yet, I don't know where you've been. I've enjoyed this one many times.

Comedy (including Romantic Comedies)

Groundhog Day (1993)
Rated PG-13
Starring Bill Murray
Director: Harold Ramis

Probably my favorite comedy (romatic or otherwise) that I've seen in a long time. Bill Murray is at his best. A cute plot that Murray handles just wonderfully.

Shakespeare In Love (1998)
Rated R
Starring Gwyneth Paltrow, Joseph Fiennes
Director: John Madden

Probably the most intelligent romantic comedy to come out in recent years. This is a cute story that is very well played. I usually don't go for this kind of movie but I found it very entertaining.

Trekkies (1999)
Rated PG
Starring Denise Crosby, William Shatner
Director: Richard Nygard

A tongue-in-cheek documentary about people a little too obsessed with a TV show. What a hoot!

Drama

Air Force One (1997)
Rated R
Starring: Harrison Ford, Glenn Close, Gary Oldman, 
Director: Wolfgang Petersen

I debated whether to put this one under drama or action. It's got plenty of action, but it's the drama that really makes it a great movie. Ford is great and most of the supporting cast is solid. 

The Fugitive (1993)
Rated PG13
Starring: Harrison Ford, Tommy Lee Jones
Director: Andrew Davis

One of the more successful remakes of an old TV series with Ford and Jones well cast in their roles. Well worth watching.

Outbreak (1995)
Rated R
Starring: Dustin Hoffman, Rene Russo
Director: Wolfgang Petersen

Suspenseful drama with a little romance thrown in about a deadly plague. Typical Robin Cook fare but well done. Hoffman and Russo are both solid.