This may end up somewhat long, but here goes!
First of all, what exactly are Action Points?
(I just took the time to add this to the official wiki :D @ wiki )
Action Points are the method by which a character's Daily Powers are recharged. Each character has a gauge represented by a D20 in the middle of their Combat Action Bar. This gauge refills as the character gains more Action Points. When this bar is filled by the attainment of Action Points, a character's Daily Power is available for use. The use of a character's daily power depletes this gauge and a character must once again perform actions which grant Action Points to refill it. Each Class has a different set of things that cause the character to gain Action Points.
What abilities gain Action Points?
Great Weapons Fighter :
Battle Fury - Increases your Atwill and Encounter damage as well as
Action Point gain for brief period. In addition, when first activated
your Stamina is refilled. This power may be activated while moving.
Indomitable Battle Strike - Savagely strike your
target to shows your other foes the fate that awaits them. After
killing a target with this strike, you gain bonus Action Point, and
nearby enemies are briefly Marked. Marked targets take additonal
physical damage until they attack you.
Unstoppable Action - You gain 5/10/15/20/25% bonus Action
Points for dealing damage while you are Unstoppable.
Guardian Fighter :
Into The Fray - A fierce battle cry that temporarily increases your
adventuring party;s deflect chance, Run Speed, and Action Point
Ability Score Bonus:
Constitution - +1% Action Point Gain
Action Surge - Gain 2/4/6/8/10% more Action Point for damage reduced
by your damage reduction.
Improved Vigor - When less than 50% health, gain 2/4/6/8/10% more
Martial Mastery - Taking damage while not using Guard now builds
Action Points. You gain a bonus to this value based on your Damage
Bait and Switch - Jump backwards, dropping a decoy in your place. Any
enemies that are near the decoy will attack it instead of you. Gain
Action Points when the decoy is hit by an enemy.
Action Advantage - 2/4/6/8/10% bonus Action Points for dealing Combat
Cunning Stalker - While Stealthed, you build 4/8/12/1/20% more Action
Action Rush - Your encounter Powers have a 15% chance to grant
3/6/9/12/15% of your Action Point.
Thrill of the Kill - When you land a killing blow, gain .2/.4/./.8/1%
of your Action Point.
Ability Score Bonus
Wisdom - +1% Action Point Gain
Controlling Action - Gain an additional .2/.4/.6/.8/1% of your max
Action Point when you cast a control power.
Critical Power - When you land a critical hit you gain 1/2/3/4/5% of
your total Action Point. (10 second cooldown)
Prophecy of Doom - Target has lowered Defense for a medium duration,
and if target is still alive after this time, They take a large amount
of damage. If target is killed during this time, you gain a large
amount of Action Points, and this power instantly recharges.
Healing Action - Gain 1/2/3% more Action Point whenever you use a
Ability Score Bonus:
Charisma - +1% Action Points Gain
Holy Fervor - Your attacks generate 5% more Action Points. Rank 2:
+5%. Rank 3: +5%
Also, if you mouse over your AP meter while it's not full, it will tell you what fills it. Another cool thing to note, is that the Recovery mod raises AP gain by a percentage.
For example, 2,982 Recovery is +49.3% AP gain.