The Space Hamster is a pet that you can purchase at Citadel Souvenirs. Once purchased it appears in the Captain's Cabin of the Normandy SR-2 beside the entrance to the bathroom opposite your personal terminal. When you select the cage, it will come to the glass, look at you, then scurry back into its box with an audible squeak. Unlike the Fish, the Space Hamster doesn't need to be fed.
Mass Effect 3
If it was purchased in Mass Effect 2, the Space Hamster can be found scurrying around the Engineering deck of the Normandy in the same general area where Jack used to be. If caught, it returns to its former spot on the shelf in the Captain's Cabin and behaves identically to its Mass Effect 2 incarnation from that point onward.
If you obtain Dr. Bryson's Experiment, when you try to interact with the space hamster the experiment will scare the hamster when it tries to come out.
Trivia
- The Space Hamster is almost certainly a reference to BioWare's Baldur's Gate series, in which a party member named Minsc carried a "miniature giant space hamster" named Boo in his inventory. Any attempts to remove the rodent would result in an audiofile being played, the same "squeak" that the Space Hamster intones when interacted with.