StarCraft

Terran Strategy
If you happen to be playing on a Fastest Possible map, you can use bunkers to block the entry of land-bound units into your base. This, along with placing turrets on the sides of the base that can be accessed via air, is known as turtling and is effective at stopping most simple rushes.

Dark Templar Rush
Because Dark Templars cannot be seen unless in the range of a detector, they are quite useful to use before your opponent(s) get detection. However, because they are also quite high up in the tech tree (Nexus>Gateway>Cybernetics Core>Citadel of Adun>Templar Archives), it is recommended that you build some sort of defense (Cannons, Zealots, Dragoons, etc.) while teching up to Dark Templars. An early assimilator is also recommended because they cost 100 gas (and 125 minerals) each. There are too many variations of the strategy to give a specific build order.

Zergling Rush
Try to play against your opponent in a small one-on-one map that you know very well. Send your four drones to start mining minerals and order your overlord to your opponent's base (to spy on him; no race starts out with anything to attack air early; by they time a Terran player gets Marines you should have your Zerglings). Hatch 5 more drones (for a total of 9, the maximum supply availible (1 Overlord (8) + 1 Hatchery (1))) as soon as you can and order those to mine too.
 * Variation: Order one Drone to build an Extractor so that your supply goes down to 8. Hatch a drone, cancel the Extractor, and order the drone to mine again. This way, you have 10 drones with only 9 supply.

When you reach 200 minerals, order a drone to morph into a Spawning Pool. At 100 more, hatch an Overlord (it takes less time to build than a Spawning Pool and you won't need it until the Pool is done).
 * Variation: Do the Extractor trick again for another 10th Drone.
 * Another variation: Since Zerg buildings can be built on any creep (including that of another player), send a Drone to your opponent's base and order it to morph to a Creep Colony. Once this is done (probably after the Zerglings hatch), morph the Creep Colony into a Sunken Colony. Obviously, this only works if your opponent is also Zerg.

Once both (the Spawning Pool and Overlord) are done, hatch 6 Zerglings (two for each larva) and rush to your opponent. If you are lucky, you will catch your opponent totally unprepared. Try to kill as many of his workers as possible and you will be guaranteed a win. If your zergling rush fails, you will fall behind in mining resources. Most experienced players know about this rush and can defend well against it so be careful of whom you use this strategy against.

Counters:
 * Terran - Build an early bunker near your resources and place one/some marine(s) inside (repair it during the attack with an/some SCV(s), or just get plenty of Marines early. Since they have range, some marines can attack while others move backward. You can also put them behind buildings so that the Zerglings must run around the buildings, giving you extra time to fire.
 * Protoss - Build two gateways and try to have two zealots come out by the time the Zerglings arrive. Alternatively, build a Forge and some Photon Cannons, although this is not recommended.
 * Zerg - Do the same thing. Because your opponent is rushing you, you have extra time to build defense (your opponent must make units and have them run to your base). You can also get a Sunken Colony to protect your base, although some players do not recommend this as it is too defensive.

Lurker Rush
Lurkers are fun to use against Terran and Protoss because of their lack of mobile detectors in early mid-games and therefore can be used to secure vital locations early on. This is very similar to the Dark Templar rush (Protoss) except it is slightly lower on the tech tree but much more costly in gas.

Counters:
 * Terran - A Marine-filled Bunker with a nearby Missile Turret placed near your resources or a choke point. If you do not have an Engineering Bay (required for the Missle Turret), you can get an Academy (which is good for the Marines & Medics and Firebat strategies) and then add a Comsat Station to your Command Center.
 * Protoss - About two Photon Cannons placed near your resources or a choke point (if there is one) and/or Observers.
 * Zerg - An overlord; this strategy really doesn't work against Zerg.

Mutalisk Rush
Mutalisks are fast flying zerg units and can be really annoying if used properly. They are good to use against Zerg and Protoss, and maybe against Terran too. They require a lot of gas though so build an early extractor followed by another hatchery and a spawning pool. Upgrade the hatchery to a lair. Don't forget to make more drones and overlords in the meantime. Build defenses if you have to, but not too much. After lair is done, make a spire. After the spire is done, make 6 mutalisks and rush them to the enemy base. If there are no anti-air defenses near the enemy's resources, then whoopee! Kill all his workers. You can also kill his army if his troops can't attack air.

Counters:
 * Terran - A marine-filled bunker near your resources. A large marine army with medic support is also nice. Upgrade U-238 shells and stimpacks. The stimpack upgrade is also highly useful here and can of course be used liberally thanks to the medics nearby.  A fair supply of missile turrets are probably the best defense going for Terrans though.
 * Protoss - Photon cannons near your resources. Maybe early corsairs.
 * Zerg - You own Mutalisks, and Scourge.