First up! In my completely unbiased way, I must recommend this comic that I also draw:
I draw both the main comic "Project Future" and a bunch of side comics over there, and they're naturally awesome. Tapewolf the writer may have a lot to do with that!
I'd also like to say that I'm currently hosting The Dragon Doctors, a comic by my good friend Speedball and it is fantastic but also sometimes NSFW due to nudity.
And! Here's a bunch of other links to nice comics:
Anaria. A selection of beautiful furry fantasy comics!
DMFA. A furry comic about... well... lots of things!
Trixie Slaughteraxe for President. All of Thorsby's comics are just incredible, and this one is no different! Absolute top-notch worldbuilding.
Stupid Fortune Cookie, a delightful slice-of-life furry comic
Code Name: Hunter, an extremely beautifully-drawn and intriguin comic. "Sixty years ago magic and myth began leaking back into London after the Seal which kept it locked away was destroyed in the Blitz."
It Hurts!!. How to describe this one... oh, I should steal Gob's description from the site! "IT HURTS!! is a comic about a silly boy riddled with depression and anxiety named Pasqualo and how he finds his first love, a mysterious yet super kind girl named Aurora. Pasqualo also has lots of friends, including his best friend Allison who’s a dirty little munchkin and Tubsy who’s a chilled out big fat dude. Over time, strange and crazy things start happening and before you know it, the whole world changes." Really good, the twist at 100 pages is incredible.
The Non-Adventures of Wonderella. Doesn't update much anymore, but is an extremely hilarious comic about a not-very-helpful superhero.
Realm of Monsters, by Shauni! It doesn't update anymore, but Shauni is so great