I do like quite a few, but some aren't kid-friendly due to extreme violence, gore, etc., so I won't be listing those!

So, because of that, it's hard for me to make a list. I dislike leaving some out, but it has to be this way if I wish to follow the rules!
As for others I like:
Rurouni Kenshin
Cowboy Bebop
MÄR (Marchen Awaken Romance)
Tenchi Muyo!
Tenchi Universe
Rave Master (this one was kinda weird, but not bad)
Wolf's Rain
Elfen Lied
Karin
Death Note
Monster Rancher
Outlaw Star
Fullmetal Alchemist
Naruto (this one's so-so; not bad, though)
InuYasha (it was good up to a point, then it became very repetitive)
There's more, but as I stated before, can't list 'em!
Many of these, I was introduced to through Toonami (years ago when Toonami was still good, mind you) or Adult Swim on Cartoon Network. Others, I'd find out about them online and I'd try watching an episode or two to see if it was any good. And, of course, there's recommendations made by friends every now and then.
I think Monster Rancher would be the sole exception for anything, since I saw that on during the morning on another channel...I think ABC Family? Not too sure on that one.
EDIT: Added some more anime I like! (and some I had forgotten about)