Terran Strategy....

BC's
If you are playing on an island map, such as 'Island Hop', quickly get in minerals and gas and start building
a) Barracks
b) Factory
c) 3 Starports
d)Science Fac. + physics lab.
While building the 2nd Starport star the construction of battle cruisers (BC's)
Once you have 12 BC's, full research, go for the attack. 12 BC's can easily take out any base.
For protection take either a science vessel or get a comsat station to combat cloaked wraiths.

Playing as them

The Terran forces are suited for defensive play and mobility. Two barracks filled with marines, backed by two seige tanks in seige mode and a couple of missle turrets are very effective at halting the enemy advance.
To rush, do so with marines. Research the stim-pak option. Jacked up marines are fearsome. Remember that the effect is temporary, so only stim them right before they encounter the enemy. No matter how you play, the upgraded marine is your best unit. Put seige tanks in seige mode near the enemy encampment, and shell the enemy structures. Protect them well with other troops. You need marines. You need a few goliaths for anti-air. You need a science vessel to detect cloaked units.
Put ghosts in bunkers. Their lock-down missles are excellent defensive weapons against Terrans and Protoss. Be sure to hot-key some ghosts for fast selection though.
Cloaked wraiths en masse are extremely effective, but expensive. Don't let them be destroyed by nibbling at the enemy in small numbers. Remember that while a few wraiths are a nuisance, 12 wraiths can be a base-wrecker.

Playing against them

The science vessel's EMP missles will destroy Protoss shielding in the area the missle strikes. Very effective.

The vulture bike's spider mines are lethal. Seed secondary resource areas with these.

Build a secondary base in your initial base and then fly the second base to its ultimate location. Fly a barracks or factory to an opponent's island and quickly build soldiers or siege tanks to surprise him. You'll need to find an unwatched place to land though.

When attacked, use SCVs to repair missle towers and bunkers during the attack. Those extra few seconds the bunker or tower may stay alive might be the difference.

Zerg Strategy....

Playing as them

You can go for the quick win with a Zergling rush. Get about 20 and hot-key them to two groups, and then use the hot keys to move them rapidly. Keep hatching more Zerglings as the first wave attacks. You may need several waves to win. Like any rush tactic, this is usually an all or nothing gambit.

Build and upgrade hydralisks, mutalisks, and guardians. This is your basic attack force, and often all you need. Use the guardians to take out the anti-air defences. This will force the enemy to come at you. When they do, retreat your guardians and let your muties and hydras meet the flushed out enemy. For shock value, burrow your hydras and have them emerge in the midst of the enemy. Bring along an overlord or two to spot cloaked units and to spot for guardian targets.

The Zerg finesse units, the Queen and the Defiler, aren't really necessary to win. They can be quite helpful, of course. The Queen's broodling attack can be used to take out a biological-based unit like a dragoon. The Defiler's plague attack is nice for weakening powerful units like the battlecruiser. The ultralisk is a nice �terror' unit, but hydralisks in numbers are better.

Use Zerglings to explore the map and burrow in key spots to remain as scouts. Put them near neutral resources and surprise the enemy when it attempts to build that second base.

Playing against them

Playing against another Zerg opponent, build a Nydus Canal from your creep to his and instantly attack him. Use an overlord to transport a Defiler close to a Terran or Protoss base, and have the Defiler plague-attack the buildings. Terran buildings will be destroyed if not repaired promptly, and Protoss buildings will be permanently damaged to one hit point (doesn't affect their shields though).

Protoss Strategy....

Playing as them

Protoss units are powerful but expensive. Zealots and dragoons are your basic ground troops. Photon cannons, while weak, are great in numbers as they attack both land and air targets. Build them close together so several will attack at once.

The scout is your basic air unit, and is more powerful than the Terran wraith or Zerg mutalisk. Scouts in numbers can wreak havoc.

Archons are very effective units, albeit quite expensive. If you can afford them, use them.

Reavers are great at destroying structures but are slow. Best to use shuttles to get them in place and pick them up and retreat when they are threatened.

Carriers are good for base defence, although a bit slow to use on the attack if you expect to have to retreat them back across the map.

The finesse units for the Protoss are the templars and arbiters. Templars with psionic storm can be effective if there's a bottleneck into your base. Build photon cannons to slow up ground attacks ,and use your templar to storm the attackers at the bottleneck. Arbiters are great for cloaking an attack force en route, but their own uncloaked presence tips your hand to the opponent. Use their stasis to freeze a battlecruiser while the battle rages, and then when the spell wears off you can concentrate on the battlecruiser.

Playing against them

Shuttle templars near enemy crystal deposits if there's a safe area for them to land. Use the templars to psionic storm and kill the enemy workers, and then load them back up again and retreat them. Use their hallucinate spell to copy a scout and get two free units to scout the map. To confuse the enemy, hallucinate copies of archons and carriers before you attack.

Put reavers on patrol right next to your outer photon cannons. They will then target any seige tanks that attempt to set up and attack your cannons. Don't do this if your opponent is the Zerg, however.

Use an arbiter's recall spell to quickly bring offensive units to the area. This is great for bringing in reavers quickly.