There is no strategy in StarCraft

Zerg:

The 6-zergling rushs are a favorite here. Build exactly 7 drones, harvest until you reach 150 minerals (200, actually, with the 1.08 patch), and then immediateply spawn one of the drones into a spawning pool. As soon as the pool completes, spawn your three free larvae into zerglings. If you're good, you will possibly be able to waltz into someone's base unmolested and take them out, as they will have no offensive or defensive units other than SCVs/probes/drones. This REALLY pisses people off.

The lurker drop in Brood War is another favorite. It invovles packing several overlords full of lurkers and then dropping them into an un-protected area of someone's base. Doesn't work, unless the victim is complacent enough to leave a hole open for the attacker. Once in, they can wreak havoc pretty much everything. Only detectors and psi storm seems to really effectively neutralize this.

Terran:

Utilize Siege Tanks to shoot across rivers and other obstacles. Eventually, use siege tanks whever you can possibly fit them. Ignore all units except marines and siege tanks. Works well on people who don't build mobile defenses, since the tanks can pick off photon cannons, loaded bunkers, and sunken colonies with ease.

Build lots of wraiths, squads of 12, and equip with the cloaking upgrade. Anyone without a viable air defense is susceptible to this. Any hole in their detection/anti-air will allow you to slip in unnoticed. Once in, take out their SCVs/probes/drones and then proceed to kill their command center/nexus/hive so as to perform a hit-and-run. Evacuate as soon as they go after you, and repeat the procedure every 5 minutes until they begin swearing incoherently at you.

Build 20 battlecruisers. Nuff said.

Protoss:

Zealots are sickeningly strong, so build 12 of these as quick as possible and send them to any fairly weak Zerg player, they will rip him to shreds. They are pretty much effective against anything, but most deadly early in the game. After a while, replace them with dragoons to do more damage.

Use corsairs to stifle all air attacks while building tons of carriers yourself. Use observers to help pick off wraiths that get in your way. Supplement base defense with dragoons and photons. The sooner you can begin crushing the enemy, the better.

The reason for the lack of strategy in most Starcraft games is twofold: rushing and "Big Game Hunters".

A rush attack, meaning a quick attack before the enemy can build his defenses, can end SC games within 5 minutes. This means that the majority of units never come into play because it takes more than five minutes to get to them on the tech tree. The more advanced units would offer "magic" abilities and more tactics, which would immensely contribute to the complexity of the strategies needed to play. Look at xmatts writeup above for a closer description of rushes.

The other reason is that something like 80% of Starcraft games are played on a variant of the "Big Game Hunters" map. These maps usually feature absurd amounts of resources right next to the starting point of every player. This eliminates the need for expansion bases. Also, there usually is a straight land route to the enemy base(s). This eliminates the need for scouting, since everybody knows how these maps look like. It also eliminates the need for air transports.

Because of these two reasons, most Starcraft games are usually short and bloody affairs with everybody pumping out lots of basic units and attacking en masse. You hardly ever see an island map (where the starting bases are separated by water) on Battle.net. Such a map makes rushing impossible, and is played with more complex strategies. The words "no rushing" (or similar) are also scarce.

As an aside: I know people who don't play Brood War because they say it's too complex for them!

If anybody is interested in a long, drawn-out affair on an island map, contact me. Theoretically, I really like playing Starcraft (not that I am any good at it anymore), but I hardly do, because rushes are boring.