I like having real world animals thrown into the mix. It gives Hyrule and surrounding lands and/or dimensions a little more of a connection to our world. Of course, having fantastic animals around (Remlits, Loftwings, cow-pigs, dragons, etc.) is great to show "this is a fantasy world" but when you overdo it and have fantastic animal counterparts for every niche, you can get to wonder why anything resembling humans is even there...
Take Pokemon, for example. It's a fun universe, but it tends to get annoying not seeing much in the ways of normal animals around, too (there are a few, fish at least, from what I remember seeing). It's especially jarring when you know that Pokemon are technically a single species. I read an article on Cracked the other day making fun of this, proclaiming that Pokemon were really invading aliens who'd come to wipe out and replicate native speices. You can really get that feel when humans are the only things on the planet that are "normal" and don't have superpowered prize-fighting abilities. Even more so when there are human-like Pokemon. I'm hoping that if I ever watch the anime again or play any of the new games, I'm going to see a cat in it and you have the option of asking an NPC what kind of Pokemon it is and they say "No, just a cat."
Watching the Star Wars movies gets like this, too. You can't have normal cows even though you have Earthlike humans in the galaxy far, far away. Nooooo! You have to have giant cow-pig-tick-things. And desert wooly-creatures that give blue milk.
I think any fantastic universe that doesn't explicity have rules or narrative devices *against* mundane animals can benefit from having a few around. One of my favorite things to do with Twilight Princess Link was to enjoy playing fetch with puppies and cuddling cats. (Then asking their opinions in sacred wolf form). See? The mundane can be *made* fantastic without turning cows into wandering tick-things.