Here I list some of the units you can get in Legion. I have most of the Celtic and Roman units up... For the rest, you can look at the screenshots. Or buy the game and see for yourself.

Roman:

Legion

These from the backbone of the Roman army. Their high armour and good morale means they will last a very long time on the front lines. They are very slow, however, so you want them in the thick of the fighting. Otherwise, by the time they move into position, the battle will be over. A training ground is necessary to produce these armies.

Praetorian

Arguably the best Roman unit, these are essentially Legions with increased morale. They require an imperial residence (very expensive) before they can be built.

Auxilia

The standard Roman unit. They are significantly faster then Legions, so if you are trying to flank the enemy's army, use these guys instead. They cost a lot of Iron (but little else), and require the blacksmith.

Cavalry

A fast moving unit with average armor and morale. These are excellent for flanking your enemy. They are unbelievable against archers, routing them quickly. Thier weakness is against units such as hoplites. Get them into the enemy army's back lines, if possible. Cavalry require a stables for production, and take up a lot food, among other things. There are many different types of cavalry in the game, and they can recruited by other nations, too. However, their differences are small. The picture you see here is that of an Equite.

Auxiliary Archers

One of my favorite units. They are much better then tribal archers, as they have more armour and higher morale. This means the can hold their own against melee for a few extra seconds. If you manage to protect them and keep them in the back lines, though, they will rain down damage on the enemy. You need a fletcher to produce them, and they take up a lot of wood-- no iron.

Velite

Not a good unit at all, in my opinion. They are essentially archers who are attracted to the front lines... not a good combination. Actually, their stats are even worse then those of archers. No wonder they only require a lumber mill to build.

Gladiators

Really good units for each person in their group... The problem is you get about half as many men as you would in a regular army. But each gladiator is as good as a praetorian. They require the gladiator school for production.

Celtic:

Celtic Fanatic

This is the Celts "level 3" unit. They have no armour, but really high speed and morale. All in all, they are a very useful unit, good for flanking but not for open line-to-line combat. Good in forest of other terrain obstacles. To build them, you have to get the warriors hall.

Celtic War Band

The standard Celtic unit, they are a lot like Roman Auxilia-- except that they are not as ordered, and cannot make many useful formations.

Tribal Archer

Exactly the same as Auxiliary Archers, only they have lower morale and armour. Still usefull.

Tribal Javelinmen

Exactly the same as Roman Velites, but they cannot use "ordered" formations.

Other:

Hoplites

Hoplites are technically a Greek unit, but you will find them around the maps anyway. They are great against cavalry, and rarely break formation. Put them on the front lines or where you want to hold the enemy back the longest (to protect archers, for example).

Peasants

These can be built by all nations, as long as you have a farm in the city. They are the weakest unit, but still incredibly cheap. They only cost food. A Little about the Units:

About the units in general:

One big difference between Roman and Celtic armies is organization. Most Roman unit types are considered "ordered," whereas most Celtic troops are considered "irregular." Ordered troops have more formations they can use, and are more tightly packed-- they are better. In general, Roman troops are heavily armored, but lack in speed. The Celts are the other way around. In battle, you will see an icon next to the unit picture. It will start out green. When the unit is engaged in melee combat, it turns yellow. It becomes orange when the group is in disarray, and red when they are retreating. High morale means the unit will take extra losses before retreating. When you win a battle, all your soldiers gain experience. They move up levels, and veteran fighters are a lot stronger then new recruits.

The pictures are from this site.