These are the webcomics I look at on a daily or regular basis:
Sinfest: The Webcomic To End all Webcomics
This one is probably the simplest. You don’t need any special knowledge, or to stay up to date with the comics.
These two are running storylines, so some reading will be required if you want to catch up. You’d also benefit from some knowledge of D&D and other RPG games.
Questionable Content: New comics every Monday through Friday
Running story arc, but you won’t lose much by skipping it. This guy has been slowly improving ever since he started, and every day he gets a little bit better.
Schlock Mercenary, by Howard Tayler
One of the longest running stories on the net, this will keep you entertained for months if you start from scratch. Good artwork and storyline.
xkcd - A webcomic of romance, sarcasm, math, and language - By Randall Munroe
My favourite, and without a running story arc, but does require a lot of background knowledge of science, maths, programming, and general geek culture.
Enjoy!