If we're talking about comic strips, the most I read is xkcd every few months - strips have never really been that interesting to me.
Otherwise, I really only bother with online graphic novels. I used to read them quite often, but most of the ones I enjoyed ended, or are on an indefinite hiatus, and I haven't really hunted down any others in the meantime.
Some of what I read/have read:
Inverloch, and
The Phoenix Requiem, by Sarah Ellerton (finished). These were amazing, especially Inverloch, because you get to witness Ellerton's growth as an artist, going from below-average work to gorgeous panels, lines, colors and composition. She was famous for producing 3-4 pages a week in full color (and did an amazing job).
Inverloch was my favorites, and a real inspiration for an aspiring artist.
Directions of Destiny by Hans Tseng (a.k.a. Slimu). Done in back-and-white in a more traditional manga style, and reminiscent of the feel of
Revolutionary Girl Utena (although so far a completely different story) - unfortunately this guy hasn't updated in forever, though he claims to be eternally working on the project.
HERO by Hwei, which until last month hadn't updated in like a year. It is one of my favorites. Atypical storytelling format, but compelling art and an intriguing story with interesting prose. The whole thing feels extraordinarily introspective. This is probably my favorite
heart , strange as it may be.
Haru-Sari by Min Kwon. Updates regularly, but I actually haven't read it in over a year. Kind of out of the loop, but what I did read was pretty good. It's just hard to get back into without starting from the beginning, because of the complexity.
The Meek by D Helmer. Apparently on Hiatus (the best stuff always is). This story was pretty awesome, even though so far it's only just getting off the ground. An interesting combination of serious and funny. Unfortunately, as mentioned, it hasn't been updated in a while.
Delilah Dirk and The Turkish Lieutenant by Tony Cliff. I only just discovered this recently, and it will probably be the thing that gets me reading online again. It's an action adventure, but delightfully non-European as near as I can tell.