House pets or any other animals that depend on you for their food, must be fed - even on Shabbat - before one starts eating.
Animals that do not rely on humans for their food may not be fed on Shabbat, and one may not even throw them leftovers, with the exception of stray dogs.
On Shabbat, one may not feed pigeons as they are capable of fending for themselves.
The Kitzur Shulchan Aruch (quoting the Be'er Heitev) holds that the custom to put out grain for the birds on Shabbat Shira (this week) is incorrect, since birds do not rely on humans for their food. He allows one to put out grain for them before Shabbat.
Other Rabbis disagree, and allow the Minhag of feeding birds on this Shabbath.
One may feed silkworms on Shabbat.
Source Kitzur Shulchan Aruch 87:18
Thursday, 8 Shvat 5775
Kitzur Shulchan Aruch:
Aruch Hashulchan 324:
The Maharal MiPrague: