Some comments on each class

Death Knight
Not a great choice for a multi-box tank. Their damage spikes make them harder to keep healed, and their more complex rotation takes more of the player's concentration away from their alts.
Pretty much unusable for ranged DPS.

Druid
As a main, they make for a good tank.
Decent ranged DPS.
Should be a good healer for the tank, but their only AoE heal spell has a long cooldown.

Hunter
Good ranged DPS. Has multi-shot which can be used for AoE whilst on /follow. Plus pets do good DPS when on /follow as well, as they are more or less automatic.

Mage
Good ranged DPS; a fireblast/fireball macro will go a long way. Polymorph is easy to macro and makes for a good crowd-control if you don't want to try AoE tanking.

Paladin
Most multiboxers swear by Pally Tanks, as their AoE tanking makes it easier to keep aggro on everything.
They also make for a good healer for the tank, but have no AoE healing for the party.
Poor ranged DPS as their only two ranged spells both have cooldowns.

Priest
A very good healer for multi-boxing, as they have AoE healing to keep the party healer.
Decent ranged DPS, and they get a channeled AoE spell which they can use on /follow at level 75.

Rouge
Can't tank, heal, or do ranged DPS. A no-go for PVE multi-boxing really.

Shaman
Good ranged DPS.
Good as healer; Totems provide AoE poison cleansing and a chain-heal on the tank can give some healing to the rest of the party in a pinch.

Warlock
Should be the same as a hunter. Only difference is that Seed of Corruption hits more targets than multi-shot and does not have a cooldown, but is not available until a higher level.

Warrior
Should make a good tank in theory.

(Note I've not actually tried multi-boxing with a Warrior, Death Knight or a Warlock so I'm just guessing in these cases.)