Hmm... where to start? What things interest you? Do you like video games and thus maybe gaming webcomics? If so I shouldn't even need to mention Penny Arcade.
http://www.penny-arcade.com/comic
But sometimes webcomics are amusing even if the subject matter isn't to your taste... I enjoy a baking webcomic called Ginger's bread. And a sewing comic called Knit Princess.
http://www.knitprincess.com/?p=3
http://www.gingersbread.com/comics/1/
(linked to the first comic in each of those on account of how story driven they are).
XKCD is not story focused and is educational and sciency, and quite worth reading through over 1000 comics for. (and if you mouse over any individual comic strip it has a second punchline)
go to XKCD.com now!
If you like a slice of life type comic that's heavily story focused I recomend Questionable Content.
http://www.questionablecontent.net/
You should start at the beginning. Even though it looks like a**, and is slightly dull at first, the joke payoff is important.
And many more... Manly guys doing manly things, Critical miss, League of super redundant heroes, Order of the stick, Las Lindas...
That would keep you way too occupied without even bringing up Eerie cutties, crazy sunshine, or flaky pastry.
And not including comedic stuff that ISNT a webcomic. Like the weekly short by Loading Ready Run, an infrequent 'Hey Ash, whatcha playin?', or the frankly excellent intelectual deconstructions by the GameOverthinker and ExtraCredits...
There... I trust I will never see you again. Ever.
razz