I like sentient animals, and I like anthropomorphic, bipedal humanoids who resemble animals. Primarily, I like the idea of animals being "Uplifted" by magical or scientific means to relatively human intelligence as in David Brin's Uplift novels. I have no problem with a race that superficially resembles an Earth animal, such as the Kzinti from Larry Niven's Known Space. I see no problem with someone wanting to pattern a fantasy race off of an animal-headed Egyptian deity or Greek monster. I also have nothing against bipedal rodents like those in Brian Jacques' Redwall.
That said, the Anthro animals in Savage Species are not terribly well balanced, and I would look elsewhere for inspiration. Arcana Evolved has five anthro races (Lion and Jackal folk PCs, Vulture, Frog, and Goat men as monsters), and Oriental Adventures has two (Nezumi and Vanara) which are reasonably well balanced against those in the PHB.
As for the rest of the poll's options...
I do however have a problem with creatures that require me to juggle multiple statblocks as they shift between several forms, or worse yet, which can infect PCs with a template that grants them a level adjustment in the middle of the game. I especially dislike the idea of a disease that causes your moral outlook to shift drastically from bloodthirsty monster to stalwart champion of justice or vice versa just because the character was unfortuante enough to fail a fortitude save. I further dislike the notion of a PC who could theoretically infect, knowingly or unknowingly, dozens of people over the course of a campaign with such a life-changing condition. So, no, I don't like Lycanthropes or other Therianthropes.
I also object strongly to the notion that a person who has a disease mating with an uninfected human can produce a hybrid species that breeds true and carries on the beneficial traits of the disease with few negatives. I know that sometimes it can be beneficial to be a carrier of a disease (i.e. sickel cell anemia carriers can be resistant to malaria), but the animalistic traits of a Shifter are going a little too far. No thanks. If however, you come up with some better fluff for Shifters, they're fine.
I also have issues with the fact that every time anthropomorphic animals pop up in conversations, someone has to make a joke about the "Furry" sexual fetish, or else associates all such creatures with said fetish. There is nothing inherently sexual about letting an animal think and talk, or giving a humanoid creature animalistic features. There is nothing overtly sexual about a child watching the Ninja Turtles, or someone reading the Man-Kzin Wars. Certainly, people can go there and think that, but everything in existance is potentially someone's kink. Just because some people have a thing for footwear doesn't mean I'm going to stop wearing shoes, or make sex jokes every time someone brings up shoes in conversation. I'm not saying this to be accusatory, and I make no moral judgements about anyone's preferences, I'm just saying that I don't feel that way about anthropomorphic animals, and I don't see a reason to pooh-pooh the idea just because someone else does have a thing for them.
Robert "Greed, Wrath, Pride, Envy, Gluttony, & Sloth Are Welcome At My Game Table, But I Keep Lust In The Bedroom" Ranting