Benefits of Multiple Pets

You want multiple pets for multiple purposes. A bear is great for solo grinding, but for PVP they're practically worthless. A cat is good for damage output, but they can't withstand much of a beating. You also want different pets with different resistences on them for end-game content (pre-BC). I don't know about level 70 content. Also, different pets have different abilities, some of which are very good, others of which are not so good. They're also good for some things, and not for others, etc.
My stable pre-BC:
-Wolf with max fire resistance: Useful for MC, Ony, BWL, and grinding dragonkin.
-Cat with moderate shadow resistance and damage buffs: PVP glass cannon.
-Bat with max nature resistance: Useful for AQ and for grinding elementals.
For levelling, you have one of two options:
1) Keep the same pet from 10-60, hence having some sense of accomplishment and loyalty that some people like. Levelling with two pets is generally a pain in the kister, though. So if you want a pet for a different purpose (other than your pet), my advice would be to tame a new one at your level, and put Fluffy in a stable. Either that or you might find a new skin you like, then tame it and have a nice looking pet next to you.
2) Tame new pets every few levels (like every 5-10). You can try new pets and see which ones you like, which has the benefit of not having to level them (just tame one at your level), but the disadvantage that it takes a lot of time to get training points.
-Potomos wrote: The signal of the hunter is as a great arrow of destination above your head that means the risk imminent.
Varrah (sex changed from Varek): 79 druid, Anetheron
Lortho: 70 Hunter, Anetheron