To me, the death of a fictional animal follows the same rules as a fictional person. If it was just some random common background character, i hardly blink an eye. Wolves, bandits, dragons? All free game in my book. However, if it was a (almost always named) character that i had actually gotten attached to... Well, let's put it this way; after playing though all of Borderlands 1 as Mordi, there were some events in Borderlands 2 that i... didn't enjoy. And i think that experience actually led me to enjoy the game that much more, because i became more invested in the game, on a more personal level.
It's really not that different from getting attached to a TV or movie character, or even an RP character. Yeah, people will tell you things like "it's just a game" or "It's not real", but i'd be more concerned for my mental health if losing someone i cared about, real or not, was not upsetting in some capacity.
(Looking back on what i just wrote, i feel this turned into more of a point about CHARACTERS in video games, but who said those characters couldn't be animals? After all, in Fable II i left thousands of people to their death just to bring my dog back to life!)