The contest runs until June 16, which is Monday, so get your picks in quick at the following URL (link to entry form and rules):
http://connect.afi.com/site/PageServer? ... weepstakes
In case anyone is interested, I've included my picks below, along with some of my reasoning. Maybe look at 'em after you've made your own guesses (not that I expect to win anyway).

Spoiler
I based these mostly on how well the various films have done in past lists of this kind, with the possible exception of my pick for the Western.
Guess the #1 ANIMATION --Snow White and the Seven Dwarfs (this is the classic pick, although "Beauty and the Beast" and "South Park: Bigger, Longer and Uncut" were sorely tempting)
Guess the #1 COURTROOM DRAMA -- To Kill a Mockingbird (based on Atticus Finch being named the #1 hero in a past list)
Guess the #1 EPIC -- Gone With the Wind (I was torn between this and "Schindler's List")
Guess the #1 FANTASY -- The Wizard of Oz (also considered "It's a Wonderful Life")
Guess the #1 GANGSTER -- The Godfather (how could I not pick this one? BTW, Part II is listed under "Epics")
Guess the #1 MYSTERY -- Vertigo (because of its very high placement on the revised top 100 list, though for my taste it was too high on the list)
Guess the #1 ROMANTIC COMEDY -- Annie Hall (can't say exactly where it's been on previous lists, but Hollywood seems to love it)
Guess the #1 SCI-FI -- Star Wars (Episode IV: A New Hope; this part is in parentheses because to me this movie will ALWAYS be simply "Star Wars")
Guess the #1 SPORTS -- Raging Bull (filmmakers seem to worship this movie, though my personal, sentimental fave is "Field of Dreams")
Guess the #1 WESTERN -- High Noon (just cuz I like it so much; I know "The Searchers" ranked highest in the top 100, but I don't know why)
Guess the #1 ANIMATION --Snow White and the Seven Dwarfs (this is the classic pick, although "Beauty and the Beast" and "South Park: Bigger, Longer and Uncut" were sorely tempting)
Guess the #1 COURTROOM DRAMA -- To Kill a Mockingbird (based on Atticus Finch being named the #1 hero in a past list)
Guess the #1 EPIC -- Gone With the Wind (I was torn between this and "Schindler's List")
Guess the #1 FANTASY -- The Wizard of Oz (also considered "It's a Wonderful Life")
Guess the #1 GANGSTER -- The Godfather (how could I not pick this one? BTW, Part II is listed under "Epics")
Guess the #1 MYSTERY -- Vertigo (because of its very high placement on the revised top 100 list, though for my taste it was too high on the list)
Guess the #1 ROMANTIC COMEDY -- Annie Hall (can't say exactly where it's been on previous lists, but Hollywood seems to love it)
Guess the #1 SCI-FI -- Star Wars (Episode IV: A New Hope; this part is in parentheses because to me this movie will ALWAYS be simply "Star Wars")
Guess the #1 SPORTS -- Raging Bull (filmmakers seem to worship this movie, though my personal, sentimental fave is "Field of Dreams")
Guess the #1 WESTERN -- High Noon (just cuz I like it so much; I know "The Searchers" ranked highest in the top 100, but I don't know why)