SCV:
This is your the worker unit of the Terran Army. Unlike the other races, this worker has a notable 60 HP as compared to 40 HP of the drone and 20 HP / 20 SP of the probe. They have the ability to repair any Terran structure, and any Terran mechanical unit. The more scvs repairing, the faster the structure/unit will be repaired.
Marine: The marine is the most basic military unit of the Terrans. When used in numbers of 12 or more, they can overpower most units. They do normal damage making them very useful against any unit. Also they can be produced very fast at at a cheap cost. Though strong in numbers, they lack armor and hit points, making them very weak to everything. When inside a bunker, the marines attack range is increased by 1.
Firebat: The firebat is the terrans counter against zealots and zerglings. They cause concussive damage and can affect more than one unit in their flame. Also very useful for air drops into worker lines. Not useful against anything else.
Medic
The medic is the healer of the Terran infantry. She's very useful for any army consisting of infantry. Medics are also very low on the AI attack script, making them the last targets the enemy will try to attack. She can also be used to heal stim packed units, making defense with stim pack possible. Other uses are blinding enemy detectors and dropships, and removing parasite and lockdown.
Vulture: The vulture is the fastest unit in the game with the speed upgrade. Having a concussive range attack, the vulture is ideal to kill small units. Theoretically they could kill any melee unit in the game, given enough micromangement. They make great scouts by themselves, but with the addition of spider mines, they're the Terran's early scout. Spider mines are best used to cover drops and choke points. They're also best if hidden in mineral sites to keep tabs on your enemy.
Siege Tank: The siege tank, is the Terran's artillery. The tank, when in siege mode, has the longest range of any unit in the game. Though it's sight is slightly shorter, a simple scout or comstat scan can be used to make the siege tank fire. Though their attack is explosive, it still possesses splash damage, and can destroy any unit. When controlling these units, it's best to separate them, so they can cover each other, since they can't fire at close units while in siege mode. Also keeping some out of siege mode is also good to draw fire.
Goliath: With the new upgrades, the goliath is decent land attacker, and possibly the best anti-air unit. The range upgrade definatly should be considered whenever using these units. When fully upgraded, they can deal more damage to the air than any other unit for it's cost. They almost specialize in island maps, where control of the air is important.
Wraith: The wraith is a weak fighter without its cloaking field to protect it. It still can deal a great amount of air to air damge, making it useful for taking out any air targets. Their role should only be used to scout and defense. Especially on defense where your opponent must bring a detector to see your wraiths. Wraiths are too weak by themseleves, and shouldn't be used to attack. They are almost worthless on island maps as well.
Dropship: The Terran's air transport. They can't be mass produced like the zerg overlords or even cost efficient as compared to the Protoss shuttle, making them very scarce and valuable. They do hold a lot of firepower, namely marines. However their gas cost limits the amount you can produce.
Valkyrie: The Terran's air to air fighter. This ship is created just to take out scouts, mutalisks, and wraiths. Very useful to eliminate an opponent's air force. Though they are quite expensive, they are the only answer to groups of Protoss scouts.
Science Vessel: The Terran's first real spell caster of the game. Having Defensive Matrix and Irradiate, make these units very valuable. Though they are expensive, their spells are well worth it. Science Vessels should always be used in any battle. These spell casters can nullify or even kill any other spell caster in the game.
Battle Cruiser: The capital ship of the Terran's. This behemoth can destroy any unit with it's yamato cannon, though it may take up to 3 shots, to destroy another cruiser. These units are very expensive, and should only be created when you control at least 2 bases, preferrably 3. And should be repaired constantly, since nothing except yamato cannon and mind control can destroy a battle cruiser instantly. A fleet of 10+ cruisers can easily win a game.
Ghost: Ghosts are the counter for anything in the game. With the ability to cast lock down, they possess the ability to stop even a battle cruiser. Not only do they have cloaking, they can also gain a sight greater than most detectors, making them ideal scouts. And with the new nuke building time, they can cause plenty of damage given, 4-5 nuclear silos. Best used on island maps, or very large maps.