In this section, the term 'furry' refers to the depiction of anthropomorphic animals in media (artwork, stories, music etc); and/or, media which affects you on a personal / emotional / spiritual level.
Angua from Terry Pratchett's novels. Reganne from "The Silver Wolf" by Alice Borchardt. Florence from Freefall. Coyote from "Pollen" by Jeff Noon. Red Stephie from "Crushed: The doomed kitty adventures" at SuperMegaTopia.
I don't have a huge collection of furry artwork, a few hundred images collected from fur.artwork.misc, and web sites, a handful of prints. My tastes tend to encompass all of the above - what I look for is good "observation" and style, and pieces that have a deeper personal significance. Very little is what might be called erotic. I do find plump furries attractive, so there are a proportion of these, but not exclusively.
The well written sort. From the above list, cy/sci-fi, adventure, humorous. I wouldn't read something because its violent or erotic, but I like those things when they are an integral part of a story.
I can't think of many furry films, "Antz", perhaps "Wolf", and "Who framed Roger Rabbit". Other films skirt around the concepts associated with furriness for me, like Alien Resurrection, Blade Runner, The Fifth Element. Less significant to me personally, but still very enjoyable are "The Jungle Book", "Lady and the Tramp", "The Aristocats".
I've always liked cartoons and animation, a brief sampling would be: The Herb Garden, Hector's House, The Clangers, Scooby-Doo, Danger Mouse, The Animals of Farthing Wood, Creature Comforts, A Grand Day Out, The Wrong Trousers, Cow and Chicken
Games don't occupy a huge amount of my time - probably the last furry game I played was KnightLore on the BBC micro. I suspect this may change in the near future though.
Calvin and Hobbes, Ruppert the Bear. I'm not really exposed to comic books created in or for the fandom. The only thing I've bought consistently was Hepcats. I'm also fond of Reality Check.
Freefall, Clan of the Cats, Newshounds, Sabrina Online, Zen dao Meow, SuperMegaTopia. I also read non-furry ones like Bobbins and Sev Trek. [Links]
I occasionally get round to drawing, and there are some examples can be found on this site.
I also write, though almost no one has read the results. These aren't on the web pages. More recently I've become involved more in fursuiting, so I suppose you could say this image of Chik'ki has elements of my furry art (the prothetic was made by Sandroo).
Tygger Graf, Paf, Bob Drake, Hiho, Kyo, The Brothers Grinn.
While not mainstream furry, I have to plug Jeff Noon for Vurt, Pollen, and Automated Alice. Akif Pirincci for Felidae. Alice Borchardt for The Silver Wolf (and not for Night of the Wolf).
From the assembled cast of Homestead, if asked to choose, I'd have to mention Allen Kitchen, Chris Johnson, and Plonq.
Swampy, Cheetah, Chama, Chris Johnson, Hrrunka.