As a monk almost maxed at 7200AA, I often get asked: which AA are important for monks?  Well, as usual, the answer is: it depends.
Monk AA is split into three catagories: Offensive (DPS), Defensive (Survivability), and Pulling.  As you progress, you're going to have to work on all three.  Even if you're primarily a raiding monk, and you figure DPS is you main function, you still need to live through the fight's AEs, occasionally offtanked add, etc.
Here I have a three tables of monk AA: critical, very high, and high priority.  All the AAs not listed may still be important, but not as important as the ones listed here.  This will easily take you into 2000+ AA.  Which order you get the critical ones is up to you, but I'd finish or get close to finishing everything critical before moving onto the next table.
Critical:| Monk AA Name |                          | Type |        | Group/Raid |        | Notes | 
| Ambidexterity |  | DPS |  | G/R |  | We dual wield, make no mistake | 
| Combat Agility 18 |  | DEF |  | G |  | Up to 18 is critical, drops off after this | 
| Combat Stability 18 |  | DEF |  | G |  | Up to 18 is critical, drops off after this | 
| Critical Mend |  | DEF |  | G/R |  | Healing 50% of HPs is nice | 
| Extended Crystalpalm |  | DPS |  | R |  | One of two main burns | 
| Extended Speed Focus |  | DPS |  | R |  | One of two main burns | 
| Ferocity |  | DPS |  | G/R |  |  | 
| Fists of Steel |  | DPS |  | G/R |  | Usually not a big fan of procs, but it's often and so good it makes 1HB useless on a monk | 
| Hastened Death |  | PUL |  | G/R |  | Fade every 30s | 
| Hastened Mend |  | DEF |  | G/R |  |  Mend every 30 seconds! | 
| Heightened Awareness |  | DEF |  | G |  |  | 
| Imitate Death |  | PUL |  | G/R |  | Our fade | 
| Innate Run Speed |  | PUL |  | G/R |  |  | 
| Moving Mountains |  | PUL |  | G/R |  | Incredibly nice pull/split tool | 
| Natural Durability |  | DEF |  | G/R |  | Must for any class | 
| Planar Durability |  | DEF |  | G/R |  | 3% of 60k is almost 2k! | 
| Planar Power |  | DPS/DEF |  | G/R |  | Just do this | 
| Purify Body |  | DEF |  | R |  | Cures anything, including "that pull" from the Avatar | 
| Rapid Feign |  | PUL |  | G/R |  | When FD fails, you'll wish you put points here | 
| Rapid Strikes |  | DPS |  | G/R |  | Pure quickness | 
| Shielding Resistance |  | DEF |  | R |  | This allows you to wield in secondary against nasty DS | 
| Stonewall |  | PUL |  | G |  | FD through spells | 
| Unflinching Resolve |  | PUL |  | G |  | Stun from behind when pulling = death | 
| Weightless Steps |  | PUL |  | G/R |  | Run 8 more or less | 
Very High:| Monk AA Name |          | Type |        | Group/Raid |        | Notes | 
| Armor of Wisdom |  | DEF |  | G |  | AC boosts never bad when tanking | 
| Combat Agility 32 |  | DEF |  | G/R |  | Continue to work this upward | 
| Combat Fury |  | DPS |  | G/R |  | Criticals | 
| Combat Stability 32 |  | DEF |  | G/R |  | Continue to work this upward | 
| Discordant Defiance |  | DEF/PUL |  | G/R |  | Resist stuff more often, live longer | 
| Extended Ingenuity |  | DPS |  | G/R |  | So self-buffs last longer... but more importantly, so does Zan Fi!  Huge boost! | 
| General Sturdiness 20 |  | DEF |  | G/R |  | Add some HPs to the mix | 
| Grappling Strike |  | UTI |  | G/R |  | Very handy positioning tool (think: High Priest in Sarith) | 
| Hastened Purification of the Body |  | DEF |  | R |  | For those repeating status ailments | 
| Hastened Stunning Kick |  | DPS |  | G/R |  | This, plus Masters', lowers re-use from 60 to 9 seconds. | 
| Infusion of Thunder |  | DPS |  | G/R |  | Perfect for use with Speed Focus/td] | 
| Kick Mastery |  | DPS |  | G/R |  | So much of monkly DPS is tied to the kicks... | 
| Masters' Hastened Combination |  | DPS |  | G/R |  | This plus Hastened Stunning Kick lowers Stunning Kick to 9 seconds | 
| Physical Enhancement |  | DEF |  | G/R |  | Pretty simply, helps everything defensive | 
| Return Kick |  | DPS |  | G |  | Riposte fires often, extra Flying Kicks never hurt | 
| Second Spire |  | DPS |  | G/R |  | Perfect little 10min refresh boost | 
| Sinister Strikes |  | DPS |  | G/R |  | Sweet passive boost | 
| Stunning Kick |  | DPS/DEF |  | G/R |  | If the mob is stunnable, greatly lowers the mobs' DPS output, so it's both DPS and DEF! | 
| Twinproc |  | DPS |  | G |  | For those who like to see procs | 
| Zan Fi's Whistle |  | DPS |  | G/R |  | 30% DPS boost when active, see also Extended Ingenuity | 
High:| Monk AA Name |          | Type |        | Group/Raid |        | Notes | 
| Burst of Power |  | DPS |  | G/R |  | Take triple attack all the way to 500 skill! | 
| Combat Agility 45 |  | DEF |  | G/R |  | Finish it off | 
| Combat Stability 45 |  | DEF |  | G/R |  | Finish it off | 
| Dreamlike Might |  | DPS |  | G/R |  | Raw Strength | 
| Earthern Brawn |  | DPS |  | G/R |  | Raw Strength | 
| Enhanced Aggression |  | DPS |  | G/R |  | Parses show this is not as useful as you'd think; get the STR first | 
| Extended Impenetrable Discipline |  | DEF/PUL |  | G/R |  | You'll thank me one day, when Furro asks you to "tank those four until the tanks get in there" | 
| Five Point Palm |  | DPS |  | G/R |  | This provides a nice little kick every so often | 
| General Sturdiness 25 |  | DEF |  | G/R |  | Finish it off | 
| Mystical Attuning 8 |  | UTL |  | R |  | For hybrids, this is real important; but we usually have plenty of room for buffs | 
| Punch Mastery |  | DPS |  | G/R |  | Get this nearly last; sounds weird, but only affects some special attacks | 
| Technique of Master Wu |  | DPS |  | G/R |  | This fires often at the end, and helps enough! | 
| Veiled Strength |  | DPS |  | G/R |  | Raw Strength | 
| Veteran's Wrath |  | DPS |  | G/R |  |  | 
Ok, while this isn't perfect... it's not a bad start.  Feel free to post your own thoughts here, tell me if I missed a big one, or send a /tell in game!