Taming, lore, vet, three other skills.
Or sometimes 4, depending on what you want to do.
I personally like Taming, Lore, Vet, spellweaving, magery, meditation. All skills scrolled to 120.
You can also exchange meditation and weaving for music and discord (or peace). I don't like it, but some people swear by it.
Or you can exchange weaving for eval int, but I rarely use offensive spells when playing with pets.
Or you can have archery, tactics and chivalry for extra offense (and healing via chivalry). And if you play with the numbers enough, you can add a fourth extra skill. (i.e. 110 taming, 110 lore, 100 vet, 120 archery, 100 tactics, 70 chivalry, 100 resist)
Or you can do that with swords.
Or you can have 110 taming, 110 lore, 100 vet, 100 hiding, 80 stealth, a bunch of ninjitsu (I really don't know how much) and um... what else do ninja tamers use? Never tried it, but some people love it.
By the way, 110 lore and about 105 taming is enough for good control of a hiryu or cu sidhe, and pretty good control of a greater dragon. Can't really tame them yourself, but they'll listen to you once they're yours.
And I've never seen this done, but always wanted to try it: Vampire Tamer
120 swords, 110 taming, 110 lore, 100 vet, 75 chivalry, 90 tactics, 80 meditate, 35 necromancy