These are comics in which all or most updates stand alone. You needn't know the context or storyline.
Buttersafe by Raynato Castro and Alex Culang
chainsawsuit by Kris Straub
Cyanide & Happiness by Rob DenBleyker, Dave McElfatrick, Matt Melvin, and Kris Wilson
Dinosaur Comics by Ryan North
Garfield Minus Garfield by Jim Davis and Dan Walsh
Gun Show by KC Green
Hark! A Vagrant by Kate Beaton
Invisible Bread by Justin Boyd
Married to the Sea by Natalie Dee and Drew Fairweather
Natalie Dee by Natalie Dee
Nedroid Picture Diary by Anthony Clark
The Non-Adventures of Wonderella by Justin Pierce
The Oatmeal by Matthew Inman
Penny Arcade by Jerry Holkins and Mike Krahulik
The Perry Bible Fellowship by Nicholas Gurewitch
Pictures for Sad Children by John Campbell
Poorly Drawn Lines by Reza Farazmand
Saturday Morning Breakfast Cereal by Zach Weiner
A Softer World by Joey Comeau and Emily Horne
Space Avalanche by Eoin Ryan
SUPER MEGA COMICS by Johnny Smash
Toothpaste for Dinner by Drew Fairweather
Wondermark by David Malki
xkcd by Randall Munroe
These are comics with story arcs.
Achewood by Chris Onstad
Axe Cop by Ethan and Malachai Nicolle
Dr. McNinja by Christopher Hastings
Manly Guys Doing Manly Things by Kelly Turnbull
MS Paint Adventures by Andrew Hussie