Unlike most people, I pretty much exclusively play SC teamed up with my friends against computers. And I used to fear them because they could Zergling rush me before I had any defense up; overwhelm my meager starting defenses with a Zealot rush; or break down my fragile defense with a ton of Marines and Siege Tanks. I'm sure if you're reading this you felt the same way at some point. But through 81 wins and almost 50 losses (uhh...my friends lose a lot and i quit to be nice...yeah, that's it), I've learned a perfect* strategy to follow against comps that should almost always** allow you to come out victorious. Here it is:

Ten (well, okay, more than ten) Easy Steps to Victory Over Your Computer!

Note: the following strategy is based on many games played on one-chokepoint-per-base money maps. If you play on multiple-choke, no-choke, or non-money maps, you will have to come up with your own modifications or else your own brand new strategy.

Second Note: the following strategy is long. Really long. But I've found that it works pretty well, so if you really are serious about seeking my advice in defeating the computer, _read the whole thing_!

1) Set your first four Probes to gather minerals and build a fifth Probe at your Nexus.
2) Set your fifth Probe to gather minerals; you should have 50 minerals by now, so build another Probe.
3) Have your sixth Probe build a Pylon. This Pylon will anchor your initial defense, so place it thoughtfully. Usually I build Cannons in a row in front of my choke using this Pylon, but you may want to leave room for ground units to get through. Then have him gather minerals.
4) Build a seventh and eighth Probe as the minerals become available. Have your seventh Probe gather minerals and your eighth Probe build a Forge behind your Pylon. Then have him gather minerals.
5) Build Probes nine, ten, and eleven as the minerals become available. Have nine gather minerals, ten go to your Pylon, and eleven mine minerals. Ten will be your builder.
6) As soon as your Forge warps in, start building Photon Cannons around your Pylon. Build 2-3 Cannons before warping in two more Probes. Then build 3-4 more Cannons. If you were fast enough, even a Zergling rush was hopefully not fast enough to beat down your Cannons. If you are extra worried, you can alternate between Cannons and Zealots, building Cannon-Zealot-Cannon-Zealot.
7) With 5-7 Cannons, start warping in Probes to mine gas. How many is up to you. When you start stockpiling gas, begin researching Shield upgrades at your Forge. Also try to max out your mineral gathering speed by building more Probes to gather. Note that you shouldn't do this all at once - try to stretch it out while building other things.
8) Starting now, things are less rigid as to how you should build. As soon as you have enough minerals, build a Gateway. When that warps in, build a Cybernetics Core. While this is happening, increase your defense with Cannons or, if those are too expensive, Zealots and Dragoons.
9) If you forego ground units for defense, you will have to rush for the next part in case there are Terrans with Siege Tanks. Once your Core warps in, you should already be mining gas and have stockpiled enough for a Citadel of Adun and Stargate. Build both, preferably the Citadel first. Start researching upgrades (Air Weapons first, then Air Armor) at your Cybernetics Core.
10) Once the Citadel warps in, build a Templar Archives. When the Stargate warps in, build a Fleet Beacon.
11) When the Beacon warps in, begin researching the Carrier capacity upgrade and build a Carrier at your Stargate.
12) When the Archives warp in, build an Arbiter Tribunal. Research Psionic Storm at the Archives and queue two High Templar at your Gateway.
13) When the Tribunal warps in, queue an Arbiter at your Stargate. Then, if you have enough minerals/gas, queue another Carrier.
14) Build a Robotics Facility and a second Stargate. When the Facility warps in, add an Observatory then a Support Bay.
15) If you were really really fast (it takes practice), your Carrier and Arbiter should come out before a Terran computer has Siege Tanks and Siege Mode.

From here you should be equipped to do just about anything. However, be warned that this is a very defensive strategy, so you will be required to sit on your butt while the computer pummels you until you have a rather large force to attack with. Usually I build a couple more Stargates and attack with 12 Carriers + 2-4 Arbiters + 2-4 Observers. But you can go anywhere with this. As long as you defeat the computer, since that was the whole point of this strategy!

* - "Perfect" as long as you work fast enough.
** - Even if you are fast enough, sometimes luck will just not be on your side.

CreepColony's Opinion: Comps = Stupid