Two separate questions:
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What were the best comic strips of all time?, and
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What are the best comic strips still in publication?
“Best” as in most innovative and/or artistically valuable? Or “best” as in personal favourites?
Current: Get Fuzzy
All time: Calvin & Hobbes #1 best evar!
Of course I have to agree with Calvin and Hobbes being the best ever!
Use both, if you wish.
Oh, I almost forgot…
Please give reasons for your selections.
In terms of comedic value I’d probably pick ** Garfield, ** (the older strips) I don’t think any comic made me laugh so hard.
These days I enjoy reading ** Calvin&Hobbes ** and ** Non Sequitur. ** Reasons? Well there’s no comic strip out there even close to being as imaginative and original as C&H. As for Non Sequitur, I guess I just love political cartoons and thoroughly agree with all their viewpoints. 
Chances are, you’re gonna hear a lot of "Calvin and Hobbes"s and "Bloom County(?)"s. I’ve only read C + H, pretty good. It was also good that rather than have him drag it out for the next twenty years, otherwise it would’ve become unfunny, stale and keep the new cartoonists out of the newspaper coughpeanutscough. “Better to burn out then to fade away.”, as Kurt Cobain said.
Currently, I enjoy Foxtrot and Robotman(when I can find it). With Foxtrot, the guy can actually draw, can actually do punchlines, and can be “dramatic” whilst still having a comedic tone.
Forgot something:
Bill Watterson(creator of Calvin and Hobbes) decided to end his comic by himself, because he felt that the comic was taking on a more “political tone” in the later years, and also because he wanted to be remembered for his quality work. I think he recently released some more Calvin and Hobbes that was unblished.
Robotman is funny in an odd way, hard to explain.
You’ll also probably hear a lot of far sides. Farside, Calvin and Hobbes and Bloom County are really popular on the board. I believe that all of them were also ended by the creators decision, too.
Another vote for Calvin and Hobbes
You can have a Calvin and Hobbes strip emailed to you each day.
Sign up at www.ucomics.com
Current? Zippy the Pinhead
Best ever? Zippy the Pinhead
Chubby Checker ate a cheese sandwich in Duluth.
Life is a blur of Republicans and meat.
Are we having fun yet?
Can’t top the old Zipster!
Pogo was utterly brilliant for the entire decade of the 50s. It declined a bit after that, but at its peak there never was anything to touch it.
The Spirit had some of the most innovative art and fascinating stories of any comic of any time, but it was really a comic book story packaged in with newspapers on Sundays rather than a true strip.
For artistic excellence you have to go back to the 1930s, when comic strips could have half a Sunday page to splash drawings across. I don’t really have a personal favorite since I’ve only seen a few pages, but everything from Prince Valiant to Flash Gordon did beautiful stuff.
Most comics today are one-joke affairs that are boring beyond belief. Doonesbury is really the only great exception.
Calvin and Hobbes. Ceased while still fresh, had great carachters, amazing art andtons of creativity.
Well, that pegs me to a tee. 
<i>Calvin and Hobbes</i> is the greatest comic strip ever. But <i>The Far Side</i> is better than <i>Calvin and Hobbes.</i>
Listen with your soul, Grasshopper.
My current favorite is Sluggy Freelance, but there was already another thread on online comics, so I’ll discount those for the moment.
Garfield is the most consistently funny, and actually has fairly good artwork, I think, but if you’ve read the first 8,000, you’ve read them all. I also have to give props to Dilbert for filling a niche that had been screaming to be filled and doing it well. Calvin and Hobbes, though, is the overall best.
Oh, and I must get something out of my system: I. Hate. Marmaduke.
Calvin and Hobbes is the greatest comic strip ever. But The Far Side is better than Calvin and Hobbes.
Sometimes, greatness defies logic.
One of the things that sets Calvin & Hobbes and Pogo apart is the drawings themselves. They are done with a brush, not a pen. This makes them much more expressive. Think calligraphy: best stuff is done by brush, Kelley and Watterson are artists first.
Best everyday comic today; The Boondocks
All Time Best Single Panel: The Far Side
All Time Best Strip: Calvin and Hobbes
Best Current Panel: Bizzaro
Best Current Strip: The Piranha Club
OR MAYBE “SHERMAN’S LAGOON.”
Peanuts, Garfield, Bloom County, Calvin & Hobbes, Shoe, The Far Side, and Dilbert.