I'm sure it differs by level range, but 2 pet classes usually do well together. A beastlord is a fun partner. They can slow, melee, heal and offtank an add.
A shaman or necro are also good choices. I've had great luck pairing up with both of these classes.
I hesitate to duo with the tank classes because of their need for heals.
Druids are fun, but would not be my first choice. I tend to try to kill mobs as quickly as possible so don't really take advantage of their dots.
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cleric would just be a bot sitting there doing a little rooting, and healing of the pet from time to time. not much fun for that cleric if you ask me.
Actually I think clerics have fun pairing up with me. Aside from the occasional heal on my pet, it's one of the few situations where they can nuke and melee (without being told "heal me", or "you should be medding"). Makes a fun change for them. Probably not the most efficient duo, but they definately don't "bot" when I've paired up with them.