These are strips that either I still follow or used to follow. Needless to say, I enjoy or have enjoyed these strips immensely. Also, all of these, with the exception of "The Far Side", can be found online.
"Garfield" - It was the first comic strip I started reading in the the newspaper at a fairly young age. I know some don't like it but, trust me, to me, as a kid just learning to read, it was simple and great.
"Pearls Before Swine" - It mixes anthropomorphic characters with funny and strange word play, funny. Talking animals that are are funny, so guess what, I like it.
"Non Sequitur" - A mix of weird, political and always funny. Plus it mixes formats from single panel to traditional with ongoing characters.
"Brewster Rockit" - It combines the comic strip medium with scifi satirical story lines. I like comic strips, scifi and satire, not surprisingly, I like it.
"Red Meat" - As far as I'm concerned this is the undisputed champion of the weekly-alternative-free-newspaper comic strips. Off the wall crazy. Greatness.
"Doonesberry" - The first, as far as I know, ongoing comic strip focusing on political and social issues exclusively. Still great.
"Boondocks" - Where Doonesberry couldn't/wouldn't go, it did. Sadly, its run was relatively short.
"Dilbert" - It's hard to believe no one had taken on the task of making fun of the mundane corporate life of cubicle dwellers. Well, this strip did it. And Dogbert is awesome.
"Get Fuzzy" - We have 2 cats and 2 dogs. The "hero" in this strip has 1 cat and 1 dog. So, I connect to it. As far as I'm concerned the best comic strip today.
"Peanuts" - I know some folks think it's old-fashioned and not relevant anymore. But, I think if you go back and read the strip sequentially back in its heyday from the 1950's till the 1980's (when strips inspired by Peanuts rivaled or surpassed it) you'll find it deft and socially relevant on many levels.
"The Far Side" - It's The Far Side. Nothing was quite like it before or after. One panel of absurd hilarity. Brilliant.
"Calvin & Hobbes" - For many this is their favorite strip. For me it's a close second. It reminded me that there are serious issues and things out there but you have keep them in perspective and remember to be silly.
"Bloom County" - My favorite hands down. It had everything, a talking penguin and his friends including a drugged out cat, a Vietnam vet, a politically aware kid and his friends and boatload of other characters. It was alternately socially relevant, weird, irreverent, political, immature and serious. I loved it. When the final incarnation of this strip "Opus" ended I was truly saddened.