Hoo wow. This threat went through a REALLY bumpy road. But anyways, I'll try to list of anime's I find ACTUALLY related to furry.
VS 40 & Knights Lamune - An early 90's anime. Allegedly in the second half of the series, the protagonist turn into furries and there were some clips to confirm. Good luck with finding them online. The episodes used to be on youtube, but I can bet the studio or company had it removed before I could watch them...bunch of jerks.
Bleach - Who could forget the fox captain? The downside is that he only appears occasinally in the anime. Secondly...the last plot arc dragged sooooooo long.
Devilman Lady - Some of the monsters just so coincidentally bear similarities to anthros. You get a demonic feline-woman (Not a cat girl! I mean fur and muzzle, I bet that makes you happy Wolfox and Impact) A shark girl. Some insects. For some reason a mix between a cat, a bug, and man. Then a bear for a few minutes. Then another feline girl side character (not neko) who was sadly gunned down in one episode) And there were other interesting monster designs. Did I also mention that the main protagist can turn into a muscly demon chick who's naked most of the time?
Fullmetal Alchemist: Brotherhood: Suprised nobody mentioned this one. There are several characters called Chimeras would could turn into anthro beings. One can become a lion, another a gorilla. I think the other ones were a a boar and a toad. Just look up "Heinkel" on google, that's a manly anthro right there.
Outlaw Star: Mentioned before, which one of the characters is a cat girl. But allegedly they can transorm into more feral creatures. I do recall one episode with a big Lizard officer.
Angel Links: Spin-off of Outlaw Star. In my opinion...it wasn't very good. But that Lizard officer from Outlaw star is a main character that has his badass moments.
World Destruction (Sands of Destruction): Apparently you people don't like this series for some reason. I'm just stating this out there because I have to. Personally, I find it so-so.
Blue Submarine No. 6 - Again, why did nobody mention this. One of the main antagonists is a shark (I...think) leading half animal hybrids against mankind. You have these fish women (not mermaids perse) with one character called Mutio. And I do recall a minor wolf character who mostly spoke in verse and poem, I dunno, that one character stuck to me. For some strange reason the main villain (if you can call him that) reminds me of Dr. Moreau for creating the chimera race.
Spring and Chaos - For some reason the creator depicted all the characters as anthromorphic cats rather than the humans in the original story, by the same write who wrote the Night on the Galactic Railroad. There seems to be a lot of symbolism in this story which I don't get to this day. If you find it, get the japanese dub....the english was...eh...
Night of the Galactic Railroad - Mentioned before, where the protagonists are cats. Again, a lot of symbolism, but the scenes are very artistically appealing considering the time it was made.
Dance in the Vampire Bund - One of the characters is a werewolf, and he has a fight with a weretiger in one episode.
Unko-G - One of the main characters is a feline demon of some kind. Good luck finding the series though.
Claymore - You get a lion character for a couple of episodes.
Animal Crossing: The Movie - Don't hate me, I'm just laying it out there...
Birdy the Mighty - A lot of the alien races the characters encounter happen to be anthro's in most episodes.
Escaflowne - Cat-girl nonewithstanding, there were other anthro races in the series, including a dog character named Jajuka who was in a few episodes. The movie (though not to my liking) featured beast like characters as well, although for some reason Jajuka resembled a lion in that film.
Final Fantasy Unlimited - It has a shape shifting wolf girl. But that doesn't redeem the series...
Guin Saga - Semi-related. The titular character has the head of a leopard.
Guyver - Well...some of the monster had interesting designs...
Hyper Police: Mentioned before in this thread.
Legend of Crystania: Throughout the movie, the inhabitants has the ability to turn into anthro beasts. From Lions, to tigers, to bears, goats, lizards, etc.
Phoenix - One story arc had a man who was cursed to have the head of a wolf.
Pandora Hearts - In battle, one of the main characters can turn into an anthro rabbit.
Tenchi Muyo GXP - A harem series. One of the characters was a feline woman. There were a few appearances of that race in several episodes.
Night Warriors: Darkstalker's Revenge: Jon Talbain and Felicia, anybody?
Summer Wars - Kung Fu Rabbit, enough said.
Brave Story - There were anthro characters throughout the film. A lizard guy and a cat-girl (bordering between neko and actual anthro) who were companions of the protagonist)
Wagaya no Oinari-sama - The kitsune character stayed in human form for most of the time. But there was a werewolf arc.
Wild Knights Gulkeeva - I believe it's the closest thing we'll ever get to a full anthro series.
So yeah, that's all I know that's not catgirls or talking animals. Some feedback would be appreciated if any of you think these were good suggestions.