Toy Story: 250 times.
Shrek: 200 times.
Finding Nemo: 100 times and counting.
Something else that father and son can both agree on: priceless
Others that (almost) made the grade:
Incredibles: a bit too violent for him.
Shrek 2: too contrived for dad (WTF with the cat switching sides so fast – and where was the dragon during all this???)
Toy Story 2: meh.
Madagascar: kid loves it, dad hates it.
Monsters Inc.: Scares the child, bores the dad (after 10 viewings, otherwise pretty good).
Bugs Bunny Superstar. Kid will like the wabbit, dad will like the backstory. Plus, it has Orson Welles in it.
Transformers: The Movie. Surprisingly good for this type of movie, and what kid doesn’t love big robots? Plus, it has Orson Welles in it.
George Pal did lots of stop-motion animated stuff, usually with a European toys theme. Track it down. In a fashion, it’s as amazing as Pixar, especially to a two year old.
Kiki’s Delivery Service
Castle in the Sky (Unless you’re a Spanish speaker at home)
My Neighbor Totoro
Porco Rosso
Nausicaa of the Valley of the Wind (borderline on the violence)
Spirited Away
and when it comes out: Howl’s Moving Castle
**Do not assume that Princess Mononoke is likewise child-suitable. **
Not Miyazaki, but…
Nadia: Secret of Blue Water
you might enjoy Utena, too. A bit surreal, but colorful enough that The Monster liked it.
Antz was pretty decent.
James and the Giant Peach–depending on how close he is to 3 anyway–it might be a bit much for a 13 month old.
And a BIG second for Iron Giant, great movie.
Likewise, Fraggle Rock is out on DVD - might be suitable for younger viewers than the Muppet Show.
China Guy, are you referring to The Adventures of Milo and Otis? If so, I heartily second that one. Great movie. (Cheap too! I may need to pick up a copy for myself.)
Also Faerie Tale Theatre is also out on DVD. I have fond memories of this series, but I don’t know how well they hold up 20 years on.