The animal forms like Cow and Spider are intended as curses, but they each have their own play styles, so some players enjoy playing as animals full time.
Unique Opportunities
There are unique opportunities for animal players. For instance, if you're playing as a Cow, Deer, or Pig, seek out the "Suspicious Looking Cow", an NPC cow in the fields of Eltibule. She can sell you some animal-specific abilities, and even has a unique dye recipe that is otherwise unobtainable ("drab grass green"). Werewolves should look for Sanja the wolf, in the forests off the coast of Kur. And every animal player will find it helpful to talk to Flia, a fairy in the wilds of Serbule.
Animal Woes
Observant players have noticed that it's hard to craft gear for animal-cursed players. There's only one gem that covers all animal curses, so you often craft Deer gear when you really want Spider gear, and so on.
In the next update (edit me), there will be a way to inscribe runes into those gems, so that you can attune the gem to one specific animal curse. You'll want to get your Sigil Scripting skill to level 25 to be able to use those techniques.
Returning to Human Form (temporarily)
In order to make "being an animal" a viable path through the entire game, the next update (Sept 2014) adds some high-level Words of Power that can help. These Words apply an illusion to you that makes you look like a human for a minute or so -- just long enough to talk to NPCs that ignore animals!
Completing quests this way is a fairly laborious process, because you have to research the Words and each Word is usable only once. It is intended that being an animal is a hard play style. The "human form" Words of Power just ensure that animals can access important skills and equipment that they will need at higher level, even though it will be a bit of a pain.
Available Beast Form
The following Beast Forms are currently available in the public alpha version of the game: