I mainly grew up with the 90's cartoons (particularly Spider-Man and X-Men).  For Western Cartoons, I would recommend these:

[b]90's Spider-Man / 90's X-Men[/b]:  These have a huge nostalgia factor for me but they are still good nevertheless.  They are also good at different things.  X-Men adapts many of the "classic" X-Men story arcs, while Spider-Man allows anyone to just "hop in".

[b]The Spectacular Spider-Man[/b]:  I never saw this until recently but it is pretty good.  I would never admit its better than 90's Spider-Man, but some have made that claim.  Very nice reimagination of the character.

[b]Wolverine and the X-Men[/b]:  Despite only being one season long, this was a pretty solid TV series.

[b]Avengers: The Earth's Mightiest Heroes[/b]:  The most recent one on this list.  Still bitter that they canceled this show for Avengers Assemble.  [b]*face palm*[/b]  You can tell from the final episode that it was cut off too soon.  >.<

[b]Young Justice[/b]:  As you can tell, I am more of a Marvel guy.  While I have not seen all the episodes for this series, from what I can remember it was well done (and I have heard the same from others who have).

[b]Batman the Animated Series[/b]:  Probably held as the pinnacle of superhero cartoons.  However, someone with more DC knowledge would have to go into more detail because my childhood memory of the show blends it with Batman and Robin, which was also in the same era.