OK, Here are some of mine.
Despicable Me
Unpopular opinion and Illumination hate aside, this movie is the strongest of their filmography and is a fun and sweet movie about fatherhood that I enjoyed a lot. (That, and I saw it for my birthday a few years back.)
The Lego Movie and The Lego Ninjago Movie
LEGOs are some of my favorite toys of all time (that I still collect to this day) and the movie managed to take a premise that sounds like it'll be terrible and turned it into one of the most visually unique and smartest animated films in a while. Also, the Ninjago Movie was a lot of fun, even if it was just okay at best.
Castle of Cagliostro
Only recently saw this one a few months back with my dad and sister through a special screening. It was a lot of fun and it was great to see one of the more influential animated films in theaters.
Prince of Egypt
Someone else already mentioned it as well. I loved this film so much that my friend just straight up gave me his copy because that was the only film I wanted to watch at his house. Also, still the best and most accurate religious/Christian movie out there and it was made by the guys who made the Bee Movie. So, step up your game plan Christian film makers! 
Anyways, those are some of my favorite non Disney/Pixar animated movies. Thanks for reading!