This is an interesting question that I'm sure most people have thought of at one time or another.
I'm going to put a slight wrinkle into it for the purposes of my post below -
What is the best 3 box if you going to be completely self sufficient (rp freak!)? So if you don't have a cleric, no asking for a HP buff in PoK. If you don't have an enchanter, no KEI. If you don't have a necro, pally, or cleric, no rez. And so on.
What would be the best three box for that?
It would be all about balancing needs, in that case. Do you NEED someone to rez, or do you NEED someone to port? Is it worth losing dps for increased utility? Do you choose three very narrow but powerful classes (ie. warrior, cleric, wizard), each one doing what they do very well, or do you choose 3 utility classes that would have more options but perhaps kill slower / be less durable? And how do you rate something like ports (a convenience, but a VERY nice one) vs resurrections (you'll eventually make back the xp anyway, and isn't useful if nothing goes wrong, but do you really want to eat a level worth of deaths on a bad night?).
So what would you want in a typical 3 box? Let's see ...
Pulling. DPS. Healing potential (I include slow / attack debuffs in this). Rez. Ports. Snare. Buffs. CC. Wipe prevention (not having to start from scratch if you die). Stuns. Tracking. Resist debuffs. Utility (invis, etc). Tanking. Mana regen.
Which are the most important?
1) Pulling. In a three box, you need to minimize mobs in camp. Even two mobs (unless you are vastly overpowered for the content) can overwhelm even the best three boxer.
2) Healing potential. Again, unless you want to always fight in easy content, you're going to need healing potential. You lose when your HP runs out.
3) Tanking. Unless you always fight non-summoning mobs, you're going to need a tank for actual challenging content.
The way I see it, the rest is fluff. You don't NEED a port - you can always run. You don't need wipe prevention - just start again (or don't die in the first place!). You don't need tracking. These are all 'nice to haves', and should definitely be considered, but only after the first three things are taken care of.
DPS is the only real variable here. Yes, the secret to 'winning' EQ is not dying before the mob you're fighting runs out of hit points. But if it takes 6 minutes to kill one mob (two clerics and a paladin?), is that really having the optimum three box? So you do need some dps, but not at the expense of the top 3 items, listed above.
So with that in mind, I present my 'completely self sufficient 3 box'.
1) Paladin
2) Shadowknight
3) Shaman
Paladin = rez + stun (damage mitigation) + backup heals + dps vs. undead + hp / ac buffs + tanking.
Shadowknight = puller + dps + mana regen + tanking + snare.
Shaman = buffs + heals + dps + CC.
While having two tank classes might seem strange, you get the following:
Increased survivability (if one tank drops, the other can step in and perhaps win - in the end, the shaman should always be the last to die, and can always cotw the rezzer back if the pally drops)
Increased healing potential (snare + stun = no mob hitting camp unslowed and 0% chance of the shaman having aggro)
Low to Mid range dps (the paladin would tank and the SK would dps) - This wouldn't be over the top dps, but it wouldn't be rock bottom either.
Mob specific dps (vs. undead obviously)
Anyway, just my thoughts for a unique scenario, as well as a unique 3 box combo.