I've seen half a dozen or so animes, generally I touch series if I'm somewhat sure I'll enjoy it.
I'm really not into the more "dbz"part of anime, unrealistic combat/w.e parts are fine but there is a small step from stylish to "power level" obsessed dick waggling contest of plot devices.
If I'd have to make recommendations which hadn't been made a hundred times already:
"Akagi". The anime revolves around Akagi
(hoho) Shigeru who is one of the most interesting protagonists in the animes I've seen. The story revolves mainly around his exploits into the underworld gambling and his dealings with yakuza in the post-ww2, dark side of Japan. The story kept me interested at all times and the games of mahjong were unexpectedly very entertaining. The strong points are easily a very solid storyline and an unique, unlikely protagonist.
A warning needs to be said though: you do need a healthy dose of patience, good taste and attention for it. Initially I had a few problems with the art style, but after I while it kind of grew on me and it actually fits the theme quite well.
It also has pretty neat OPs and EDs, really loved them.
"Sayonara Zetsubou Sensei" series. It's a peculiar comedy anime about a charismatic, depressed high school teacher and all his fellow misfits which conveniently happen to be his pupils. The anime is episodic and goes on about various random aspects of life, society and Japan in general. It's very entertaining and I could probably recommend it anyone with a sense of humour, at least for a few episodes to see if you like it. I have a bit hard time describing the show well, the wiki article probably does it better. Very entertaining, "light" material which doesn't take anything too seriously. Stylish animation too. Guess a warning should be that it's rather Japanese-y and that somewhat decides how much you will like it.
Also happens to have great OPs and EDs, also very enjoyable.
GITS
Cowboy Beebop
