The virtual pet “era” is now past the Tamogotchi phase which consisted of keychain-sized computers with digital characters (which ranged from the generic "dog" to any cartoon character or celebrity) that you could interact with in a very finite (and often small) number of commands. The "pet" would react to these commands in exactly the same manner every time.
Now there are computer software versions that exhibit signs of artificial intelligence such as learning "tricks" and showing preferences. These games provides a rather expansive list of interactions such as: toys to offer the pet, different foods to feed the pet, clothes to dress the pet, and scenes for the pet to play in. The pets in these games act as if they have free will (i.e. can refuse the food, show preference of one food over another, or even use the food in a non-intended fashion-- such as batting the dish of food around).
Such games that I know of are Catz, Dogz, and Virtual Monsters.