The question is, are they pets or are they familiars?
Well, certainly cats and toads have always been on the list of familiars, and while I haven't heard of owls or rats, neither seems particularly unlikely. Indeed, my first thought was, "Oh, familiars. Neat."
And many stories and rpgs seems to go along with that thought. It makes perfect sense in a school of witchcraft and wizardry, doesn't it?
Let's say that everyone is right. Here's what I would expect, then:
1. Animals would be required along with books, robes and cauldrons.
2. They would be used in some form of classwork.
3. They would be referred to as familiars in the course of the books.
4. There could be no subsititute.
None of these conditions are true. Hermione doesn't get Crookshanks until her third year, and we don't hear about animals for Ginny or the twins. Nor do we hear about adults having animals other than the elderly Errol.
We never see them used in class, except for Snape's use of Trevor that one time, and that was cruelty, not magic. The only ones truly used at all are the owls, who are the most popular because they are so useful. But if one does not have an owl or doesn't want to use one's own, there are public owls available - the owls in the Hogwarts Owlery for the students and teachers and the ones in the Hogsmead Owl Post Office. Also, people quite happily borrow owls from friends, which does implies ownership but not connection.
And we never see them called familiars - the word doesn't appear in that sense in the books. Pettigrew calls himself a "pet" ("Haven't I been a good pet?") and earlier, Ron tells Lavendar, grieving over her lost bunny, that Hermione doesn't "care about other people's pets." His use of "other people's" implies that she does care what happens to her *own* pet - Crookshanks.
I've already addressed the exclusivity issue - Harry can use Pig or any of the school owls as well as Hedwig.
I can also knock down these arguments: familiars need not be required, just permitted, for example, and those with familiars will learn how to make use of them (other than as postal owls) when they are ready, presumably in sixth or seventh year. Just because Rowling doesn't use the word doesn't mean that they aren't familiars (just like the whole "wards" thing - she may call them protection charms, etc, but they're still wards.) And whose to say that one can't use another's owl just for mail purposes?
However, until we see differently in books 6 and 7, I think the evidence as presented in the books points to the animals being pets, with owls as particularly useful ones.