Hmmm, my tastes in cartoons are older than I am - I like many of the old B&W cartoons. Back when I watched television I would tune in to Sunday Night Black and White on the Cartoon Network.
I am fond of much of the work of the Fleischer Brothers, some of the best animation ever made. Gabby the Liliputian made several appearances outside of the film Gulliver's Travels. Popeye and Betty Boop were other famous characters from the brothers.Part of my appreciation for these films is the animation itself... much higher than is common today.
I have had bad experiences with anime - disliking the plots of a majority that I have seen, and hating the low frame rates and poor tweening. A major exception has been Miyazaki - who has done some incredible work - high frame rates, good tweening, coherent plots, and characters who grow over the course of the films. Spirited Away is one of my favorite animated films of all time, third behind Snow White and Gulliver's Travels. A friend of mine very nearly forced me to watch My Neighbor Totoro, and I am glad that he did. Another made me watch Dragon Ball Z... one of these days I am going to kill him in his sleep.
Everything I hate about anime rolled into one.
From television the original Johnny Quest was one of my favorites, and at times is downright Spycrafty.
Other favorites have already been mentioned, I will add the original (psychotic) Woody Woodpecker, Droopy, and Who Framed Roger Rabbit.
The Auld Grump