I don't remember what my first webcomic was, since it was a medium I went hogwild on for awhile on.
These are ones that I remember reading in 2004-2006:
Chugworth Academy by Dave Cheung and Jamal Joseph Jr. (Not sure if this one is entirely appropriate, skimming through it on the Internet Archive right now. Edit: Yeah, no. Aged really badly.)
Rachel the Great by Rachel Naboors (when it was on girls.com lol)
VG Cats by Scott Ramsoomair
Cyanide & Happiness by Rob DenBleyker, Kris Wilson, Dave McElfatrick and Matt Melvin.
Questionable Content by Jeph Jacques
Death and the Maiden by Nina Ruzicka
Charby the Vampirate by Amelius (gorey and maybe inappropriate, so fair warning)
Zap! by Chris Layfield and Pascalle Lepas
I also read The Devil's Panties Jennie Breeden, but I totally forgot about it until I saw it in this thread. And she's a mom now.
I'm going to have to catch up on it.
In a way, a ton of these webcomics inspired me to start my own, but I got the final push from Lore Olmpus by Rachel Smythe.