I've always really liked animation. I have dozens of animated movies on DVD, and a whole lot on VHS too. I'm hoping the VHS ones are still ok when I'm able to take them out of storage!
I like stop motion as well as cel/CG type animation. I have a lot of anime but also a fair amount from other countries. It would be very difficult to say what I thought the 3 best animated movies were, depends on the phase of the moon and such :-). Off the top of my head, for movies I would probably say:
Akira (better story with subtitles, although the English dub is good)
Ghost in the Shell
The Incredibles
but if I wasn't limited to 3 I would insert a bunch of Studio Ghibli movies which I really like (just watched Princess Mononoke the other night :-), Wallace and Gromit, Ray Harryhausen movies, Patlabor, the Disney Robin Hood, some other Pixar movies etc. etc. etc.
I won't really explain my choices there too much. Akira and Ghost in the Shell are classics. I really like The Incredibles not just because it's got great animation and story but also because it reminds me of the sense of fun that James Bond movies have lost since Pierce Brosnan started. It's my modern James Bond substitute :-).
I'm also going to add my 3 favourite animated series, which is kind of different to movies. Those would be
Futurama (I have 4 or 5 seasons on DVD plus the movies)
Cowboy Bebop
The Adventures of Tintin (the Ellipse/Nelvana ones from the early 90s are excellent. I thought the recent Tintin movie was pretty awful)
Closely followed by some others like FLCL, Trigun, Creature Comforts, Ghost in the Shell Stand Alone Complex, Aeon Flux, Duck Tales (haven't seen that for a long time mind you), and quite a few others. Lots of animated series I don't like. Plenty of Japanese ones are just animated soap operas. There aren't many western ones which go beyond comedy, and I find many of the ones which aren't just aimed at kids pretty ugly (Family Guy and spin-offs for example).