Many of the webcomics I read have been listed here, like:
QC
XKCD
Scout Crossing
Something Positive
I'm also a fan of:
Girls with Slingshots
Invisible Bread
Crazy Sunshine
The Devil's Panties (has a pretty sizeable archive, dating back to 2001)
Two Lumps
Bridges
Teahouse (18+)
Mahou Shonen Fight!
Everblue
PrinceofCats
Cans of beans
My reading taste is pretty varied!
There are other comics listed here by others that I haven't had a chance to look into yet, but have been meaning to. Gunnerkrigg Court is one example.
Girl Genius is my third most favorite. It's a bit difficult to get into at first, since it just throws you into a situation where you aren't connected to the characters, so it seems uninteresting for a little while. However, if you become interested, and work past that point, you will find quirky humor, a creative world, and many deeply fleshed out (if OP 
) characters.
Girl Genius I never got into, quite likely for the reason you mentioned above, where I didn't enjoy it from the very beginning. It didn't grab my interest and I tried reading it for I think nearly 30 pages
I'm willing to try again, because I know a lot of people do think very highly of it, and it seems like the sort of genre I would enjoy. I just couldn't get into it at the start.
