Daicon III
This was the very first anime from Gainax, and you'll notice is that they used a lot of copywritten stuff in this and the sequel. However, they weren't threatened with lawsuits, but couldn't release it stateside. As for copyright laws and Tom telling people not to use music in their CD/mp3 collection, this article by the Cato Institute sums up my thoughts on that issue.
Daicon IV
The aforementioned follow up to the above featuring Electric Light Orchestra's Twilight
Mighty Mouse
This is what Terry toons was best known for and I like the Musical/Action mix that they had at times. Too bad Filmation's version sucked, but Ralph Bakshi knew how to do it justice.
Woody Woodpecker
I grew up on this crazy bastard when NBC aired Walter Lantz' classics aside from Oswald the Lucky Rabbit. Unfortunately, the new show bored me to hell in spite of being true to its source.
Tom & Jerry (Van Beuren version)
A lot of you may think of MGM's Cat and Mouse, but Tom & Jerry started out as a couple of policemen back in the 20s-30s.
Superman (Fleischer Bros. version)
This may be well-known when compared to most of the subjects posted, but damn it, I still consider this to be the gold standard in action-adventure animation.