I acknowledge the desire to pinpoint specific strategies, but such strategies are not the key differentiation between a good 1v1 player and a good 2v2 player. Most of the other answers on this question have touched upon this point to varying degrees: At the end of the day, the strategies used are the same (rushes, early expanding, building a defense at a choke point that guards two bases, flank attacks, etc). The key difference is that you have the benefit of delegating your attention to only part of your army while your teammate covers the other part.
StarCraft 2 is balanced for 1v1 play. What that means is that the goal is to make 1v1 about the skill of the players. Sure, each race has their advantages and disadvantages, and map features have quirks that may more easily be exploitable by one race as opposed to another, but overall 1v1 is about pure StarCraft 2 skill. To be the best, you have to understand the ins and outs of both your race & the other races (including build orders and typical strategies).
2v2 is different. Sure, two very skilled players should do well in theory. In practice, they only do well if they coordinate their efforts. In 2v2, a coordinated effort can break down a non-coordinated effort by skilled players fairly easily. While some people would argue that it's basically a 1v1 game with an early expansion, it's the fact that another person can notice and respond to situations, coordinate efforts, and act autonomously of your own ability to command as many units that is the hallmark difference in 2v2 play. Using that to your advantage will prove to be the largest contributor to the success of a 2v2 game where each player understands the mechanics of 1v1.
Consider a scenario where a 2-player zerg team decides to 6-pool one of the two people on the other team. Unless there is a shared defense, they will destroy the other player more often than not. In this case, the typical response is, if possible, a base-trade. If the teammate of the victim has enough of an army out, they can rush one of the two opponents in response and knock the game down to a 1v1. Otherwise, it's pretty much "game over, man".
In 2v2, it's much easier to execute more elaborate strategies if you are coordinating with another person. You could take your army and half of theirs and launch a main attack (or a feint) while your teammate flanks the enemy from another angle.
Skill plays a lower role in 2v2 games. This is one of the reasons you don't see as many high-level 2v2 games or strategies being developed. Cheese play tends to be enough of a strategy at times, and if you cheese the game down to a 2v1, you can get ranked pretty high without needing the encyclopedic knowledge of the game that would be necessary in 1v1. The result is that less effort is spent developing detailed 2v2 strategies as they are not in as high a demand as detailed 1v1 strategies.
Another aspect of 2v2 games is that they tend to be played by people who are not as confident about their skill level. They tend to be a bit defensive and rely a bit too much on their partner to bolster a mutual defense or army. This can be exploited easily with a well-executed rush strategy as described earlier. Unless the rush strategy is going against a shared and uber solid defense, it will typically do enough damage to be worth the attack. If you do go up against the uber defense (and you've scouted properly), then the economy has likely been spent on buildings or units that are less useful for an offense. This give you an opportunity to expand and eventually overwhelm your turtling opponents.
In short, if you're good at 2v2, it doesn't mean you'll be met with the same success in 1v1. If you are awesome at 1v1 and can coordinate with an equally skilled person in 2v2, you'll have a pretty solid 2v2 team. You might even win more often than not if you get cheesed and your teammate is taken out, but the fact remains that you won't be as invincible as you are in 1v1, and it's not because of your strategy. It's because, if you don't coordinate with your teammate, your opponent can exploit that and temporarily turn the game into a 2v1 battle for just enough time to cripple your team. That gets them ahead, which helps them to get "more ahead" (which is the key to winning any SC2 match).