There's a wide array of effects that powers will have on an enemy. The following list contains some of the general characteristics that powers can have.
Note that there are unique powers that do not fall into these categories, and there are some that may combine effects from multiple categories (for example, an attack that damages your foes while healing you in return).
Deal damage to an enemy — this can be damage to a single target or area of effect (damaging all targets within a given area). Total damage of some powers can be dealt up front in a single shot or in damage over time (dealing a set amount of damage to an enemy for a specific or random duration of time).
Improve your survivability in battle by making it harder for enemies to land an attack on you or by reducing the damage done when an attack hits you. Powers that boost Defense make you that much more difficult to hit; powers that increase your Resistance will make you take less damage than normal.
Mezzes & Taunts
Mezzes (short for Mesmerize) restrict your enemy's actions, whether it be preventing them from moving or by stopping all action with some form of stun effect. Some powers turn a foe against his comrades for a time.
Taunts attempt to compel the enemy into attacking you, causing them to abandon their current targets. On the other hand, Stalkers receive an ability known as "Pacify." This is a "reverse taunt," which makes enemies stop attacking you.
Buffs & Heals
Buffs improve the effectiveness of you or your allies in combat by raising certain traits, such as accuracy. Heals replenish Hit Points lost in battle.
Debuffs make enemies less effective in combat; for example, reducing their damage resistance or the rate of their attacks or reducing the accuracy of their attacks and how much damage they can do.