Azumanga Daioh
A good comedy but I'm assuming that since you know what anime is you've likely already seen it.
Eyeshiled 21
It's about football which would normally really put me off (frankly, football sucks dick) but because it's anime it automatically makes it more interesting. If you aren't the type to enjoy sports anime then this might not be for you. And if you're hardcore into sports then the fact that it doesn't have much to do with realistic football might put you off too. There's lots of slapstick and general fucking around to offset their love of football so it works out to a nice mix.
FLCL
There is a bit of drama but it's not that much. This is one of the most whacked and wacky shows I've ever seen. Only 6 episodes but it feels strangely developed. You sort of have to pay attention to understand it to its fullest but just a straight up watch will be good for some entertainment.
Getbackers
This one takes a little to get going bu it's pretty interesting. Has a strong comedy element but the story is noticeably present so it doesn't seem like a pair of guys with spiky hair just dicking around all the time.
School Rumble
Excellent show that loosely resembles Azumanga Daioh. This is probably what Azumanga would have been if it had a real plot and some continuity (though don't take that as a point against Azumanga since its a terrific show). When I first watched this show there were parts where I laughed till I cried and some of the jokes became inside things with my friends. A really great series. Has an OVA as well. It just fills in a few random blanks though. Nothing significant.
School Rumble Nigakki
Second season of School Rumble. The first ten are as superb as the the first season but then the show starts to drag a bit. Maybe it was due to me watching it as the episodes were being released and not in chunks (this is the sort of show its best to watch about 3-4 episodes at a time). Either way, worth a look if you like School Rumble.
There is going to be a third season (not 100% confirmed but I think one of the characters mentions "Sangakki" in the last episode at the very end) so thats good as well.
And thats really all I can recommend in the "Adventure/Comedy" genre. If you want some more serious anime then I can help you out. Mainly I stick to mid-teen to adult range of anime unless something specifically catches my attention.