I read a lot of webcomics, and indeed real comics (although the latter is irregularly due to financial constraints). Here's a list, if not comprehensive, then fairly complete, with added opinion.
Real Comics
Sandman
Yes, the comic that's on everybody's list. Found it through Death's manga series, but before I knew it I was swept into the magical world of Morpheus. I've read the entire main series, but I presume there's more out there waiting to be devoured. I simply can't wait. I hope to get the series in book format so I can re-read it whenever I want.
The Uncanny X-Men
I haven't got very far with The Uncanny X-Men, only to around issue 10, but it's incredibly fun. It's great seeing how my favourite characters started out, and my god was it cheezy. I'm not able to access any more at the moment, but the minute I can I'll be reading them again, mark my words.
Y: The Last Man
Quite possibly the only "last man left alive" thing that's any good. It's deep, funny, sometimes gory, usually shocking. I finished it recently, and the ending was confusing. But it was perfect too. You need to read this series.
Webcomics
To put it another way, who doesn't love Calvin & Hobbes? I read it irregularly at the best of times, but I hope to get a subscription to the website hosting it so I can read the archives. Getting the books would be great too.
Don't hate me for it! lol. Despite the hate that surrounds this comic (I believe mainly due to it's author), I completely adore CAD. Aside from the mad chef who I could happily do without, there are few times where I don't like it. I prefer the story-arc comics to the non story-arc comics for the most part, as there is a lot of humour to be got out of every day life. Though I still wonder when Ted the penguin will make a comeback.
Extra Life is... odd. Parodies games and the like, but not in the usual way. Has a slightly more... adult take on it.
Cyanide & Happiness is another comic I read irregularly. I'm not even sure why I like it, as the humour isn't to my usual tastes. However, I suppose every person needs one thing that's completely out there and this is mine. Warning: Cyanide & Happiness can be sick at times.
Garfield is brilliant and yet not brilliant. What is there to say about Garfield but
lasagne?
What could be better than Garfield? Garfield without Garfield. Wait, don't go yet! It's better than it sounds, and it needs to be seen to be believed. See Jon struggle with loneliness, schizophrenia, and bipolar disorder as he tries to get by in life. It is oh, so poignant.
I used to like GPF more when it didn't do the massive fantasy plot-arcs. To me, they didn't really fit. Maybe it's because I've matured a bit since I started reading it (a massive 5 years - I was 14) but it doesn't seem as good as what it used to be. But give it a chance, read the archives, there's a lot of good stuff in there. And maybe you'll like the alternate universe stuff more than me.
A new addition to my comic-roll, Girls with Slingshots appears to be a comic about a group of girls full of sarcasm. I've not managed to read the archives yet, so I may be wrong. I like it though.
If you like maths and common sense, and don't mind a blog, then indexed is for you. Humour that makes you think. What could be better?
Warning: if gay, bisexual, bicurious or transgender people offend your sensibilities, then this comic is not for you. However, if they don't, then you can't go far wrong with Khaos Komic. Based around romance and confusion in high school, it's nowhere near as cliché as it sounds. I've been following it since the beginning and it's wonderful. Please give it a go.
A surreal comic that's more of a graphic novel. Still not finished, but you'd do well to give it a chance anyway. I did and now I'm eagerly awaiting the next page. Has a pretty awesome rendition of Death (at least I think it's Death), though not as awesome as the Discworld one.
LICD is probably not to your usual tastes. But give it a go anyway. Underneath it's sex-mad exterior lies a soul of actually quite deep stuff. Sometimes. It is worth a go, especially if you start at when Raine meets his neice.
A World of Warcraft based comic that's actually quite good. Has a psychotic evil bastard wizard named... Richard. Seriously. Give it a shot, it's worth it.
I've only incredibly recently started reading this so I have no idea what it's about, but the past week or so's comics have caught my eye so on the list it goes.
C'mon, who doesn't read Penny Arcade? Is funny, is bang on, is a corporate
machine.
Another corporate comic about games and stuff. Is incredibly similar to GPF, with more Panda.
Less questionable than you might think. About music, coffee shops and great t-shirts. (Seriously, check out the store.)
Another recently added one, fairly random, is one-day gag based rather than story based. Is quite good.
Snafu is your tri-weekly dose of the bizarre yet true. (Or would be if it weren't fictional.) Check it out!
Sore Thumbs is hard to describe, so instead I'll use what it describes itself as: "Insane Political Gaming Manga-Type Comics". Well, there you go.
Does exactly what it says on the tin, and looks good whilst doing so.
Well I had to have one zombie comic didn't I? This is the first one I've found which is actually quite good.
Blame my boyfriend for this one. If it weren't for him I wouldn't have even tried it because I usually find furry squicky. But it's not bad. I've only got to volume 4 as of yet.
A library webcomic. Either you'll love it or you won't. I love it.
Ok, who saw this coming? I read this sporadically, which is fine because updates are sporadic too.
The grand-daddy of all geeky comics. There are no words.