Of course, over the course of leveling, I had to abandon her (leveling pets was nowhere near as easy as it is post-Patch 3.0.2) but these days I keep the company of Leech Widow from the Wetlands. Yes, it's a generic white spider, but you'll understand these things if you have a Hunter. The cool thing is, Spiders now appropriately have the Web ability that we only used to envy from NPCs. It entraps opponents for 4 seconds from 20 yards and has a 40 second cooldown. It's a damage-less version of the Exotic Pet Silithid's Venom Web Spray. The good news is, the damage doesn't really matter. You'll want to use the web merely to keep opponents at a distance. This ability makes them a great choice for Level 19 twinks.
In a perfect world, spider webs would trigger Lock & Load. It actually did for a brief moment of Hunter overpowered-ness, but was quickly hotfixed making Spiders no more ideal for Survival than any other pet. That said, spiders make excellent pets particularly for PvP, sharing the same Cunning talent tree as the previously featured bats. They're moderately good for PvE DPS, as well, with acces to the useful albeit long-cooldown mana regeneration talent Roar of Recovery. Because spiders don't really give anything particularly exceptional -- Hyenas are theoretically the best non-exotic pets for PvP because of Tendon Rip -- you don't see Hunters use them much. That should be enough incentive to tame one.
There are tarantula-like bulky spiders, spindly ones like Krethis Shadowspinner, and the Burning Crusade introduced spiders that were spindly and spiky, such as the gigantic Zarakh in Bloodmyst Isle (who shrinks ridiculously when tamed). Even cooler skins will be introduced in Wrath of the Lich King, with spiders looking webbed-up and ghastly. Unfortunately, the only truly unique skin belongs to the Azjol-Nerub boss Hadronox, who is quite unlikely to be tameable. Still, spiders are icky, creepy, and move in a distinctive skittery fashion and should be a welcome sight in the midst of all those boring Core Hounds. Spiders eat meat exclusively, so stock up lest they start using Bite on you!