With low resource costs and a decent Carry stat they are useful for raiding early on when labor comes quickly. As a city grows, laborers become more scarce and useful for producing resources in ways that don't consume them.
Fighters are a 1st row troop, on the front line. This means that they are going to be hit first by many enemy units. Fighters and Swordsmen are useful to absorb damage so units in other rows like Archers and Bowmen can continue to do damage longer. Although Fighters (and Swordsmen) will attack Hoplites first in battle, the damage output from fighters is generally too low to reliably eliminate enemy hoplites before the hoplites have done their job of damaging Cavalry. Therefore, Fighters are generally best suited as raiding units or as inexpensive first row units to protect your back row units. Expect to lose at least 3 fighters a raid just to damage from enemy Structures so plan accordingly.
All unit stats by level can be viewed at the Official Help Database
|Training Ground||Fighter · Bowman|
|Barracks||Swordsman · Archer · Hoplite · Gladiator|
|Stable||Cavalry · Knight|
|Workshop||Helepolis · Catapult|
|Trading Post||Ox Wagon|