Terran owns Protoss
Protoss owns Zerg
Zerg owns Terran

Heres the stuff to back it up...

Terran owns Protoss 1)EMP
2)Nukes
3)EMP
4)EMP
5)Did i mention EMP?

Protoss owns Zerg
1)Psi Storm
-Psi Storm can, yes can kill ANYTHING... it works best if the enemy as all his men bunch together.
2)Ummm... thats about it...
3)Well... Psi Storm, pretty much owns anything...

Zerg owns Terran 1)Dark Swarm
-Can kill anything as long as you got a good attack in there ( both ranged and melee guys )
2)Plague
-You probably never would of thought of this and if you had well... good for you. Plague the terran buildings, why you ask? they well burn to the damn ground in a couple of seconds, err minutes...
3)Broodling
-Damn, don't you just hate those damn tanks?
4)Guardians
-There annoying, there good against tanks/bunkers/turrents... back em up with hydras, hey, what could stop that?

Whew... Well all those are good, but as you can clearly see, the Zerg own the Terran, its not even a contest...

And i didn't even mention what would happen if you had an allie of the opponent race, but i'll mention that later... aiight?

CreepColony's Opinion: For protoss vs zerg, corsairs are also good for "overlord hunting".

MercilessPrick replies:

First off, Terran does NOT own Protoss. If you've never seen fast Protoss players, you should check it out when a guy goes 7 pylon, dual gates (specific build order hidden, since I use it), and sends the first zealot in. First z in ALWAYS jacks over a terran. As far as Two more zealots are close behind the first, so all he has to do is either A) Run past the bunker you built at the front or B) Hit any buildings that aren't in range of your bunker if you built it near your command center. Usually with them sending the first Z in, your bunker will just have finished and you will have a few marines (this is assuming you racked on 7 or 8. If you decide to depot, then rack, you're going to be struggling to fend off the butt pounding). One zealot can usually kill at least 2 marines, perhaps even 3 or 4 or more. Two more zealots are coming in. Expect them to come in streams of two every time. They'll make you hole in if they don't kill you (the zealots will occupy a good portion of your base, out of the reach of your bunker (which MIGHT be still standing from the begininng of the game). For those of you that say rushers suck, I'll remind you that in the top 50 ladder games many games are settled by who rushes the best. Those that say rushers suck either A) Cannot defend against it, or B) Can defend against it but don't want to because it screws over their build order and reduces the fun for them, or C) Think because they know about the 1.07 fast six zerg rush it means all rushers are zerg, and therefore all rushers are skill-less newbies. Nuke? Chances of getting that far without the protoss pounding you into the ground are virtually nill. EMP? Even without shields protoss units are killing machines. Also, chances of getting to EMP before protoss beat you silly are practically nill. Reason? Before you get EMP you will be hard-pressed to stop protoss rushers. Before you get EMP its ill-advised for terrans to stage a rush, unless its a bunker push (which on most maps is extremely inconvenient, time wasting, and money wasting. Psi storm does not own just zerg. A psi storm can still kill a terran infantry unit twice over (except the SCV, but hey). Tanks? Let's not even get that far. We will maintain the focus on the early game holing in, simply because we will assume the protoss will always hit you with the 3-4 minute Z rush. You simply cannot hope to tech climb to tanks with zealots harassing you, more coming in, and the protoss climbing the way to goons (if they don't kill you before they get there). As far as I know, even if for some reason you break their siege (whether because the tosser mis-micromanaged, you slowly bunker push your way out, or a miracle happens) if the map terrain is not in Terran favor (i.e. Temple), you usually find yourself as a disadvantaged victim.
Second off, Zerg do NOT own Terran. If you've found yourself in a position to get dark swarm before they tank you in, the Terran guy isn't good enough. Micromanagement kings use Terran to own zerg like anything. If you've never seen the "green archon" trick with Terran against Zerg, you've been missing out. You won't ever climb the tech tree high enough against Terran before being mowed into the ground.
Damn I hate it when I sit down to say something and get totally off topic. I think I was going to say something along the lines of "Rush as fast as you can" and keep the pressure on or something, but I guess this turned into a rebuke against Kiloz! or whatever his name was.

Caleb adds:

And now for a REAL Rock Paper Scissors.
strategy: Toss Ownz Terran:
1:Disruption Web.
This is great against Bunkers- Sure the Marines
can move out, but what's a Marine outside of a Bunker
to a Zealot? Supper, that's what!
Also this is good against Tanks, since they will suck
without the protection of their bunkers. It also
kills Turrets and outer defense well.
2:Psionic Storm.
If he comes at you w/t Tanks, Marines, Wraiths, and perhaps Ghosts,
create a distraction with Zealots, then quickly Psi Storm
everything. The Wraiths may move out to attack, but you made him
lose many Marines and Tanks for your one Templar-
this is even more vicious with Khaydarin Amulet!
3:Early Game Zealots.
In the Early Game, Zealots are so much more powerful than Marines!
Sure 6-8 Marines can kill 3-4 Zealots, but once you have
8+ Zealots, you will OWN. With proper micro,
Zealots devastate Marines badly, and only Bunkers can save them!
4: Dark Templar, Rushes and Otherwise.
Getting DT's Early in the game can spell death for those wretched Terrans! With good micro, you can run to his peon line, kill his ComSat, then proceed to waste SCVs. once that's done, assumng you've been massing Dragoons with range, kill the rest of him, but get his CC first! First destroy Tanks and Bunkers outside of Range, then kill everything else. Keep scouting to see if he expanded and kill it quickly. If you do not massacre him early on, it's Fool Temp Time! Attack with three or four DTs, then quickly pull out as he ComSats the area. Repeat with larger numbers of DTs and waste his ComSat energy, then move to his Peon Line for the kill!
5: Corsairs. Although I mentioned Dweb, I forgot Corsairs! These guys are fast, dangerous, and deadly. They work well against Valkyries, and make mince meat of Wraiths if you have Observers with Speed and, preferably, Sight Range Upgrade.
6: Dragoons.
"Ten marching Dragoons with Armor, Range, and Plasma Shields." 'Nuff said.

Zerg Ownz Toss:
1: Zerglings.
These guys will BUTCHER Dragoons, and a pair of them for fifty minerals with Speed is enough to kill a High Templar.
Also, you can burrow these guys in potential Mineral sites, know if they have seen 'em or not. 2: Overlords.
Dark Templar Rushes almost never work against Zerg- they see your DTs, and then they whoop them with something like 8 Hydralisks or 5 Lurkers. Ack. Also, a Zerg player will have Overlords loooong before Toss gets Observers, and Zerg can outexpand them greatly(which it will need to). 3:Devourers.
Devourers own Corsairs, and they slow the retreat
of Carriers and Scouts a great deal.
4:Defilers.
Dark Swarm with Consume can spell death for Mass Dragoons, and it gives the Zerg player a great defense against Carriers, plus (s)he can bring in Devourers :(). Also, Plague can cut thru shields. If this guy has a Terran allie with Sci Vessels and EMP.... Oooh boy......
Terran Ownz Zerg
1:Bunkers, Pushes and Otherwise.
Have you ever seen six Lings running toward a peon line in the range of a Bunker? It is such a slaughter that StarCraft should have been rated MA for cruelty to giant insects. Also, right when a Zerg player finishes a sophistacated build order, and sends his/her hi-tech units down the ramp, they discover theiris a Bunker on either side with Siege Tanks and Turrets. All units die. Then tanks unsiege and proceed to blow big messy holes in Zerg base. Even late in the game when Queens are about, this is apocalyptic- what use is Spawn Broodling when Goliaths blow your precious Queen out of the air without breaking a sweat? Even if you get past the deadly Charon Boosters of the evil Goliaths, you are assaulted by the equally perilous Stim Pack from the hated Marines!(life as a Cerebrate sucks, doesn't it?) 2:Early Game Marines.
Now, most Zerg players will scream; "But a Zergling can beat a Marine!!!!!!!!". True that may be, but 12 Lings can't beat Six Marines- here is why: Zergling runs at marine, Marine fires, Zergling tears up Marine. 12 Lings run at Six Marines, Marines start firing;Ratatatatat!There goes one. Ratatatatat! There goes two. Ratatatatat! There goes three...... You see, it's the RANGE FACTOR. You've got to consider.
Also, Marines own Hydralsiks, who only do half Damage to them. Marines and Tanks mop the floor with Hydras. Marines, Tanks, Medics, and Firebats spatter the Hydralisk's guts all over the ashy ground while the carapace is burnt to a crisp by Firebats.
3:Siege Tanks.
Siege Tanks are the most apocalyptic weapon in the game, and the main reason the Terrans can hold there own against the other races.
They have the longest range of any ground unit, and lemme tell you, they totally r0x0r the Zerg like nothin' else!! Four Tanks with support by Goliaths and Marines will do wicked wicked wicked things to Hydralisks, Zerglings, Defilers, Lurkers (with Sci Vessels), and even the 'mighty' Ultralisk.
4:Scičncé VčszéLz.
"Six science vessels floating in a Zerg base, Irradiating like mad. Two Irradiate each other and float over the Drones." 'Nuff said.