Rare spawns are an old feature in World of Warcraft, dating back even to the early days of WoW. However, most of these were simply rare pets with a unique ability (back in the OLD days of Vanilla pet training) or some slightly tweaked looks. That all changed in BC, and significantly in Wrath.
Spawn times generally are different from beast to beast, but are on the scale of hours, rather than minutes. Blizzard has not posted the the actual spawn timers for each creature, but I have seen some rare creatures spawn as quickly as 6 hours from the previous tame, to as long as nearly 24 hours. Each creature has a different spawn timer and the leng appears to be random, though there is a minimum and maximum limit. The basic point is: Be patient, your creature will spawn, eventually.
Locations are a bit tricky. Most of the desirable rare spawns tend to spawn in about three or four locations (though that changed in 4.2 with the addition of the "Challenge Tames"). Some rare spawns (Notably Arcturis, and the new Challenge Tames in 4.2) have only 1 spawn point. You would think this makes it easier, but it in fact does quite the opposite, for two reasons.
First, if there is only 1 spawn location for a rare, sought after pet, then you will have to contend with every hunter out there camping for that pet.
Secondly, the new Challenge Tames introduced in 4.2 are quite hard. I think that Blizzard would have been insane to make hunters both path out a location and go through all the different tactics to tame these rare spawns.
The location in which each creature spawns (if it has multiple spawn locations) is generally random. Some of the creatures will patrol around their spawn area, while others will stay in one location. To the best of my knowledge, these creatures do not de-spawn, rather they stay in their area until they are either killed (gasp) or tamed (yay). The following is a list of all of the Zones in which a rare creature can be found. As I write further I will have specific guides for all of these rare creatures.
Spirit Beasts: (Beast Masters Only)
Loque'Nahak (76 Spirit Leapard) - Sholazar Basin.
Gondria (77 Purple Spectral Tiger) - Zul'Drak
Arcturis (74 Blue Spectral Bear) - Grizzly Hills
Skoll (80 Lightning Saber Worg) - The Storm Peaks
Ghostcrawler (85 Blue Spectral Crab) - Abyssal Depths
Karoma (85 Twilight Highlands)
Ban'Thalos (85 Green Spectral Owl) - Mount Hyjal [The Regrowth Phase]
Ankha (85 Green Spectral Tiger) - Mount Hyjal [The Regrowth Phase]
Magria (85 Blue Spectral Tiger) - Mount Hyjal [The Regrowth Phase]
4.2 Challenge Tames (BM, MM and SV Spec)
Solix (85 Orange Fire Spider) The Molten Front [Phased]
Deth'Tilac (85 Purple Fire Spider) The Molten Front [Phased]
Skarr (85 Gem Sabre) The Molten Front [Phased]
Karkin (85 Gem Crab) The Molten Front [Phased]
Kirix (85 Green Fire Spider) The Molten Front [Phased] NOTE: not a unique skin
Anthriss (85 Yellow Fire Spider) The Molten Front [Phased] NOTE: not a unique skin
Skitterflame (85 Red Fire Spider) The Molten Front [Phased] NOTE: not a unique skin
Cataclysmicly Rare Pets: (BM, MM and SV Spec)
Sambas (85 Lion) Twilight Highlands
Terrorpene (81 Fire Turtle) Mount Hyjal
Other Rare Pets
King Krush (75 Green Devilsaur) Sholazar Basin
Olm the Wise (White Ghost Owl) Felwood NOTE: skin very similar to Ban'Thalos
Tsul'Kalu or Uhk'loc (Silver Gorilla) N. Stranglethorn and Un'Goro respectively