Terran Units and Counters:     
Here are the Terran Units you should use against the other races:

Against Zerg:

Unit Counter
Drone: Firebat, Marine, Anything
Zergling: Firebat, Vulture
Hydralisk: Marines & Medics
Overlord: Wraith, Goliath, Science Vessel (Irradiate)
Scourge: Marine, Goliath
Mutalisk: Marine, Goliath
Queen: Science Vessel (Irradiate)
Ultralisk: Science Vessel (Irradiate), Yamato Weapon
Defiler: Marine, Goliath
Guardian: Wraiths, Science Vessel (Irradiate)
Devourer: Goliaths, Science Vessel (Irradiate)
Lurker: Science Vessel (Irradiate), Siege Tank

Against Protoss:

Unit Counter
Any Unit: Science Vessel (EMP)
Probe: Firebat, Marine, Anything
Zealots: Firebat, Vulture
Dragoons: Marines & Medics
High Templar: Science Vessel (EMP), Firebat, Vulture
Archon: Science Vessel (EMP) + Anything
Dark Templar: Science Vessels (Irradiate), Air units
Dark Archon: Science Vessel (EMP) + Anything
Shuttle: Goliaths, Wraiths
Reavers: Yamato, Spreaded Marines
Observers: Science Vessels to Spot, Anything
Scout: Goliaths, Marines
Carrier: Goliaths, Wraiths
Arbiter: Science Vessel (EMP), Goliaths
Corsair: Goliath, Marine, Battlecruiser

Hope this helps in the correct use of the Terran Race.