What program is making this sound and how can I make it stop
Solution 1:
Sounds to me like the Windows Search dog.
Do you have Windows Search (press Windows-Key and F) open? It makes the same noise - I think it's the dog panting.
You could verify this by opening Windows Search and (right-)clicking on the dog. Every time I do this I get a similar noise.
As for stopping it, assuming that it is the search-dog, you could try turning off the animated character using the right-click menu on the dog.
Solution 2:
This is often the default alert sound from Windows Live Messenger. Unfortunately even if you have alerts turned off, the sound option is under the different sounds menu option:
Simpy go to: Tools > Options > Sounds > Contacts Sign-in > Don't play a sound