I just played a bunch of 3v3 games and did really well, so I thought I'd share my experiences.
The Early Attack
First, discuss with your teammates what you consider an "early attack". I played (as Zerg) with Terran and Protoss allies, and my 10-pool build gave me a LOT of Zerglings before they even had much of a force ready, because they were using builds with later attack units. As a result, my economy was much smaller, I still hadn't expanded by 40 food (which is death for a Zerg player), and though we eventually knocked out one opponent, we couldn't take on the armies of the other two.
You should NOT try the early attack strategy when your opponents have a common main. The whole idea of the early attack is to overwhelm one player and remove them from the game, turning the game into a 3v2, where even if your side has sacrificed economy for the push, your 3 economies will still beat (or at least keep up with) the 2 opponents remaining. If your early game push fails, you are going to lose the game unless you do a lot of economic damage. What sometimes happens on these big 3v3 maps is that the two attacking armies pass each other, and the game turns into a 2v2 as each side eliminates one opponent.
In another game, we illustrated the fact that if one player early expands (preferably not the one in the most vulnerable map location!) and chooses a harassment units (Mutalisks in my case), it can go very well. However, what sets apart a gold-to-platinum player from a bronze one is knowing when to switch out of the build. I've been both on the giving and receiving end of a partnership where one player massed nothing but Void Rays, and the opponent massed nothing but Marines. Needless to say, the Void Ray player loses, almost regardless of what the other two players do, UNLESS the Void Rays stay with the rest of the joint army. If they are used for defense or attack by themselves, they tend to get chewed up. What they SHOULD be used for is decimating bases and harassment.
Alternately, if you don't want to go for the big mid-game push, you can pick one player for harassment, while the others expand and tech. However, if the map doesn't have common bases (i.e. each player is spread out), this approach can leave you highly vulnerable to pushes, since you don't have much ground defense.
In general, 3v3 requires you to specialize. For example, the Protoss player could make an army with more heavy-hitting units, such as Colossi, Void Rays, or Immortals, while the Terran player goes MMM, and the Zerg player makes the meat shield of Roach. You'll frequently see things like mass ling+bane, mass hellion, or mass (blink) Stalker. Most massing strategies rely on fast units that can shut down enemy expansions and give map control such that those players can expand and switch into heavy-hitting endgame armies.
Big, High-Damage Units
The problem with big 3v3 battles is that they rarely take place in wide-open places where all units can attack. This means that if you're going for a big push, you need to have the big, high-damage units such as Colossi or Siege tanks to deal splash damage at range. Units such as Broodlords can be good (although very slow!), and anything with AOE such as Infestors or High Templar do more damage than in 1v1 or 2v2, where players don't have such a large mass of units, and can more easily micro the whole army around the AOE.
In smaller games, fixed defenses chew up a lot of resources that you could put into army. However, on big 3v3 maps, with so many opponents, the importance of denying harassment is game-winning. DO NOT expand without adding fixed defenses. At the very least, slowing down an opponent's attempt to deny expansions can give you time to call for help, and possibly even crush the opponents' combined army while they are in your territory and far from their own reinforcements.
I don't know how many times I've turned around a big army by rushing 20-30 Zerglings into the opponents' main, or an expansion. Best of all, if the opponents are controlling their armies separately, you have a good shot at dividing the combined army and then killing the smaller army with the help of your allies. If your opponents don't build fixed defenses, or even just a good wall, more opponents simply means more targets.
If you die to cheese in a 3v3, you probably deserve it. There is really no such thing as "all in cheese", because even if one player sacrifices economy to "cheese", he has two allies backing him up such that he can recover economically.
However, with the large maps and common main bases, cheese is extremely unlikely - it just doesn't arrive soon enough to be effective, and is defended too easily (even just with workers)! However, if you forgo scouting, and you get double 6-pooled, chances are that you won't have a wall up soon enough to block it out, and the game will be over. 3v3 doesn't mean you can omit scouting, or assume your allies will do it.
I've seen things like a double-worker rush, where two players send workers to attack one player, and you MUST respond by pulling your own workers to save that ally, or else you will be the next target and things will only get worse from there. If you DO pull your workers, your side will have an advantage of numbers, and in reinforcements, and you should defend the worker-attack easily and win the game. Don't fall for this cheese.