For example, if the first team says "tiger" then they erase the letter 't' and other animals beginning with 't' such as turtle can't be chosen. A member of the next team will then do the same, and so on until a team can't think of the name of an animal that begins with one of the remaining letters. The last team remaining wins!
Make sure as many students as possible have a turn coming to the front and saying the name of animal and keep an eye out for students using books or other resources who are trying to get an unfair advantage.
To speed things up a little you could let students erase not only their starting letter but also one more, which definitely makes things more difficult for the teams that follow afterwards.