That's kind of a tough question, since the speech recognition world has been concentrating on speaker
independent recognition. The two main types are the independent kind where it does a credible job with any person (although it will get better as it gets used to you) and the
dependent kind where you give it a word list, speak each word once or twice and it only recognizes you. This second type was the most common for years, but people hated going through the training - so now the best selling software out there is the independent type. Dragon Systems is the best known for having really good software like that.
Googling a bit, I found some people saying good things about a speaker dependent speech chip that you can train for 40 words (
http://www.imagesco.com/kits/speech-rec ... n-kit.html). I've never played with it myself, but it sounds promising. They sell it by itself, in a board kit you assemble (are you good at soldering?) or preassembled. In use, you say which if the words you want to train (by number) and speak it into the microphone. When you say that word again, it pops up that same number on the screen. It's designed to be used by itself or connected to a computer.
If you look for "speaker dependent voice recognition software" in a search engine, you'll mainly find companies selling products for assistive living. Some people need extra help with things and talking to a computer is much easier for some people. Folks who have speech issues may not do well with speaker independent software, so a few companies still sell speaker dependent software. One Windows program, "speak-to-me" looks interesting (
http://www.rjcooper.com/speak-to-me/) You can download it and try it free for a while before you buy it. You might even try emailing the developer (link at the top of the page) and explain your project to them - they may offer you a copy to help with your research.
Spend a few minutes in a search engine and see what you come up with. I think you'll find a bunch of them, although far fewer than you would have a few years ago. Good luck with your project! What kinds of animals are you planning to work with?
BTW - Have you heard of the "Bow-Lingual"? (
http://en.wikipedia.org/wiki/BowLingual) It was around a number of years ago. You put the transmitter/microphone on the dog's collar and the handheld receiver "translates" the barks. I bought one when our Cavalier King Charles was a puppy and it was a fun device. Unfortunately she wasn't much of a barker, so we never got much fun out of it.
Please help me! 
Thank you!