Subraces of Khajiit
Would completely fit. Plus, that means playing as sapient http://tvtropes.org/pmwiki/pmwiki.php/Main/Ptitlebwhmt6p47cy5 Note: I'm dead serious. Intelligent Khajiit that look like common house cats are in the lore.
Subraces of Argonians
Would also fit fine.
Imga
Ape men from Valenwood. They're likely very uncommon in other parts of Tamriel, but it it is not inconceivable that one ended up in Skyrim. Besides, who doesn't want to play as http://www.imdb.com/media/rm2271057920/tt0133152
Tsaesci
Snake men from Akavir. They served as advisors to the Emperor in the First Era and ruled Tamriel in the Second Era. Likely, they won't be attacked on sight like a Dremora or Sload, but won't be trusted either.
Tang Mo
Monkey people from Akavir. http://tvtropes.org/pmwiki/pmwiki.php/Main/Ptitlefr5h9p9h6i92
Kamal
Some sort of intelligent snow creatures from Akavir. Unlikely, considering they freeze in the winter and Skyrim is a bit chilly.
Ka Po' Tun
Tiger people from Akavir. We already have cat people, but hey, we also have more than one type of human and elf.
Sload
Slug creatures from Thras. The least likely, considering that they would have to design too many new animations and armor just for them. Also, do you really want to play as http://images.uesp.net/thumb/9/91/Sload_big.jpg/280px-Sload_big.jpg
Ayleids
Also called wild elves. A few still exist, scattered throughout Tamriel. They'de probably be the least out of place, but we have enough damn elves already.
Maomer
Tropical elves from Pyandonea. Would also fit, but that's still too many elves for my taste.