We've got a DS list, a PS3 list and quite possibly, a 360 list. Since there isn't a PSP list I've decided to throw one together. As far as I know we don't have a Wii list that's up to date so I might make a new one later. Although I do own a Wii myself, I'm not terribly versed in great Wii titles so if anyone else is willing to make one, please tell me!
 
With the recent release of the PSP Go!, which eliminates the UMD and therefore you can only purchase the game on PSN, I'm going to split games into a two different categories, PSP games and PSN games. Games that are availiable on both retail and download are placed into the "PSP" section whereas games that are only availiable on the PSN Store are placed into "PSN". I'm going with this format for the time being but if anyone has a better idea, just holler.
 
Like any other list, this is a community run list so comments, additions and suggestions are welcome. 
 
Update: Added some more games and included an import and upcoming section. Will reformat list later.

For a list of DS games, click here.
For a list of PS3 games, click here. 
For a list of Wii games, click here.
 

PSP

• Burnout Legends -  
• Burnout Dominator - 
• Metal Gear Solid: Portable Ops -
  
• Metal Gear Ac!d -
  
• Metal Gear Ac!d 2 -
  
• Grand Theft Auto: Liberty City Stories -
  
• Grand Theft Auto: Vice City Stories -
  
• Grand Theft Auto - Chinatown Wars -
  
• Loco Roco series -
  
• Patapon series -
  
• Ace Combat X Skies of Deception -
  
• Castlevania: The Dracula X Chronicles - 
• Disgaea: Afternoon of Darkness -
  
• Disgaea 2: Dark Hero Days -
  
• Echochrome -
  
• Crisis Core: Final Fantasy VII -
  
• Final Fantasy Tactics: War of The Lions - 
• Final Fantasy I -
  
• Final Fantasy II -
  
• Jeanne D'Arc -
  
• God of War: Chains of Olympus -
  
• Me & My Katamari -
  
• Pangya: Fantasy Golf -
  
• Resistance: Retribution -
  
• Secret Agent Clank - 
• Ratchet & Clank: Size Matters -
  
• Sid Meier's Pirates! -
  
• Syphon Filter: Dark Mirror - 
• Syphon Filter: Logan's Shadow -
  
• Half-Minute Hero -
  
• The Warriors -
  
• Valkyrie Profile: Lenneth - 
• Lumines -
  
• Crush -
  
• LittleBigPlanet -
  
• Tekken: Dark Resurrection - 
• Ridge Racer 2 -
  
• Monster Hunter Freedom Unite -
  
• Wipeout Pure -
  
• Wipeout Pulse -
  
• Star Ocean: First Departure -
  
• Star Ocean: Second Evolution - 
• DJ Max Portable - 
• Pursuit Force - 
• Pursuit Force Extreme Justice - 
• Classic Dungeon -
  
• Persona 3 Portable - 
• Metal Gear Solid: Peace Walker -

PSN

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? -
• Fate Unlimited Codes -
  

Imports

• Tales of Versus -  

Very few of those games are what I would call "fabulous"

"
 

PSP

 

• Burnout Legends -  Great
  
• Burnout Dominator - Dunno
• Metal Gear Solid: Portable Ops - Great
• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
  
• Grand Theft Auto - Chinatown Wars - Dunno
  
• Loco Roco series - I guess so.
  
• Patapon series - No
  
• Ace Combat X Skies of Deception - No
  
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure
  
• Crisis Core: Final Fantasy VII - Dunno
  
• Final Fantasy Tactics: War of The Lions - Dunno
• Final Fantasy I - Dunno
  
• Final Fantasy II - Dunno
  
• Jeanne D'Arc - Dunno
  
• God of War: Chains of Olympus - Great
  
• Me & My Katamari - Dunno
  
• Pangya: Fantasy Golf - Dunno
  
• Resistance: Retribution - Sure
  
• Secret Agent Clank - Dunno
• Ratchet & Clank: Size Matters - Hell no
  
• Sid Meier's Pirates! - Nah
  
• Syphon Filter: Dark Mirror - Absolutely
  
• Half-Minute Hero - No
  
• The Warriors - Fuck yes
  
• Valkyrie Profile: Lenneth - No
  

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

May I also suggest Syphon Filter: Logan's Shadow?

" May I also suggest Syphon Filter: Logan's Shadow? "

Solid selection there, definitely. I've been needing to pick up Badman, but I think I might just jump on the sequel instead. 
 
Also, I don't want to get into a huge debate or anything, but I never liked the LocoRoco series. It's cute, but it's not really fun to play. It could be a neat-o Wiiware/iPhone game for $10 or something (hell, iPhone has Rolando,which is basically the same thing) but as a full-fledged PSP release, it's extremely lacking.
 
Patapon on the other hand is friggin fantastic. One of the best rhythm games I've ever played, and easily one of the most stylish games ever. That music & the art style are amazing as well.
 
Lastly...Crisis Core is awesome, but I haven't finished it. And lastly lastly, get Dissidia. You won't regret it.

" @eroticfishcake said:

"
 

PSP

 

• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
• Patapon series - No
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

That's my opinion on your list. "

Bunch of recommendations: 
 
Lumines  - this addictive puzzle game is absolutely essential. Sold the PSP to many people.
DJ Max Portable - rhythm games from South Korea with a strong cult following. Fantastic series.  
Shin Megami Tensei: Persona  - a good RPG, but closer to a port than a remake. It's not to everyone's liking due to its age.
LittleBigPlanet - not played this personally, but many are saying it's as close to the PS3 game as can be. 
Tekken: Dark Resurrection - the best, most content laden fighting game on PSP. Runs at a beautiful 60fps.  
Ridge Racer 2 - didn't see a US release unfortunately. Includes all of RR1's content plus tons of extras.
Star Ocean: First Departure & Star Ocean: Second Evolution  - enhanced remakes of the classic PS1 RPGs. Maybe not essential but still good. 
Monster Hunter Freedom Unite - this has over 100 hours of gameplay and, no joke: reduced Japan's productivity the day it was released.   
Wipeout Pure & Wipeout Pulse  - and finally no PSP list is complete without Wipeout. Everyone loves these games.

" @Emandudeguyperson said:

" @eroticfishcake said:

"
 

PSP

 

• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
• Patapon series - No
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

That's my opinion on your list. "

Wut.   LCS was way more interesting than VCS. And Patapon 2 is arguably the best damn game on the system - it even won GB's PSP GOTY.  Also, you've not played half of the games! "

" Bunch of recommendations:  Lumines  - this addictive puzzle game is absolutely essential. Sold the PSP to many people.DJ Max Portable - rhythm games from South Korea with a strong cult following. Fantastic series.  Shin Megami Tensei: Persona  - a good RPG, but closer to a port than a remake. It's not to everyone's liking due to its age.LittleBigPlanet - not played this personally, but many are saying it's as close to the PS3 game as can be. Tekken: Dark Resurrection - the best, most content laden fighting game on PSP. Runs at a beautiful 60fps.  Ridge Racer 2 - didn't see a US release unfortunately. Includes all of RR1's content plus tons of extras.Star Ocean: First Departure & Star Ocean: Second Evolution  - enhanced remakes of the classic PS1 RPGs. Maybe not essential but still good. Monster Hunter Freedom Unite - this has over 100 hours of gameplay and, no joke: reduced Japan's productivity the day it was released.   Wipeout Pure & Wipeout Pulse  - and finally no PSP list is complete without Wipeout. Everyone loves these games. "

" @Emandudeguyperson said:

" @eroticfishcake said:

"
 

PSP

 

• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
• Patapon series - No
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

That's my opinion on your list. "

Wut.   LCS was way more interesting than VCS. And Patapon 2 is arguably the best damn game on the system - it even won GB's PSP GOTY.  Also, you've not played half of the games! "

" @Slippy said:

" @Emandudeguyperson said:

" @eroticfishcake said:

"
 

PSP

 

• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
• Patapon series - No
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

That's my opinion on your list. "

Wut.   LCS was way more interesting than VCS. And Patapon 2 is arguably the best damn game on the system - it even won GB's PSP GOTY.  Also, you've not played half of the games! "

This.  I hate it when people troll things out of sheer ignorance.
 
Great list eroticfishcake.  I agree with 100% of your choices.  LCS is a proper GTA game whereas VCS is more of a hey we increased the mapsize release. "

" @Emandudeguyperson:   What do you mean by not stylish enough? It's a rhythm / tactical / sidescroller / micromanagement game with great art and catchy music. I don't see how it lacks style in any way. "

I think the Metal Gear Ac!d series is better than Portable Ops (but maybe not as good as Peace Walker). Though I'd start with two rather than one since it explains the mechanics better.

" @Slippy said:

" @Emandudeguyperson:   What do you mean by not stylish enough? It's a rhythm / tactical / sidescroller / micromanagement game with great art and catchy music. I don't see how it lacks style in any way. "

 It is none of those things, it is a button masher dressed up like a sidescroller, it is also very poor and no fun to play, and if you consider black stick-men or average looking boss characters like dinosaurs to be artistic, well, you're wrong,  plain and simple, also the music was pretty much ear rape. "

" @SeriouslyNow said:

" @Slippy said:

" @Emandudeguyperson said:

" @eroticfishcake said:

"
 

PSP

 

• Grand Theft Auto: Liberty City Stories - Shit
  
• Grand Theft Auto: Vice City Stories - Awesome
• Patapon series - No
• Castlevania: The Dracula X Chronicles - No
  
• Disgaea: Afternoon of Darkness - No
  
• Disgaea 2: Dark Hero Days - No
  
• Echochrome - Sure

PSN

 

• Holy Invasion of Privacy, Badman! What Did I Do To Deserve This? - NO
  

"

That's my opinion on your list. "

Wut.   LCS was way more interesting than VCS. And Patapon 2 is arguably the best damn game on the system - it even won GB's PSP GOTY.  Also, you've not played half of the games! "

This.  I hate it when people troll things out of sheer ignorance.
 
Great list eroticfishcake.  I agree with 100% of your choices.  LCS is a proper GTA game whereas VCS is more of a hey we increased the mapsize release. "

No, have you even fucking played VCS? It fixes nearly everything I didn't like about LCS! "

I don't own many of those but this seems pretty comprehensive. 
You really should create a tier system to make it clear which games are necessary and which games are more for collectors. For example, you don't get enough out of the FInal Fantasy 1 and 2 remakes for them to really be must-buys. 
Be sure to add Fate Unlimited Codes (PSN) and Tales of Versus (import)

All the arguing about I like x game more than y game aside shouldn't this just be a list of games that people should know about? This isn't a "my top psp game list" or anything, it appears to just be a list of games people might like. All the random arguing is crazy...  
 
Moving on I suggest Tales of the World: Radiant Mythology. Has the standard Tales combat but much different gameplay with a focus on quests and such. Also as someone mentioned above the first 2 Star Ocean remakes should also be on this sort of list.

@Emandudeguyperson:
Sure, that's your opinion on those games, if you don't like them or aren't willing to even try some of them that's your choice, no problem with that. However, you're being a dick about it, and that's a problem. 
 
Dissidia is pretty decent. Tekken 6 is more of Tekken, if you liked Dark Res, that should be there too.

" All the arguing about I like x game more than y game aside shouldn't this just be a list of games that people should know about? This isn't a "my top psp game list" or anything, it appears to just be a list of games people might like. All the random arguing is crazy...   Moving on I suggest Tales of the World: Radiant Mythology. Has the standard Tales combat but much different gameplay with a focus on quests and such. Also as someone mentioned above the first 2 Star Ocean remakes should also be on this sort of list. "

" @Abyssfull: That official? "

How about Phantasy Star Portable?  Not a perfect game by any means, but a fun multiplayer loot grinder.
Second one improves on a lot of the issues too, but doesn't have a Western release date yet.

lack of Metal Gear Acid brings a tear to me eye :'[

" Lack of Metal Gear Acid brings a tear to me eye :'[ "

You should add Crush to that list.

Wait, you still use your psp for games?

" Wait, you still use your psp for games? "

" @EVO: Added. Danke! "

May I recommend Pursuit Force and Pursuit Force: Extreme Justice?

" May I recommend Pursuit Force and Pursuit Force: Extreme Justice? "

Couple more suggestions since it is a new day, mostly from the RPG side since that is just kind of my thing on the PSP. 
 
Brave Story New Traveler. I don't own it myself but it used to be talked about on other places around the net and it has some really positive reviews.  Comes off as a game that anyone into handheld RPGs could get into, and if anything it looks really nice.
 
Kingdom Hearts: Birth By Sleep and Final Fantasy XIII Agito. Both of those should be on the "up coming" for namesake alone. Both are from widely known series and even in a worst case scenario will probably be better than similar titles on the console. 
 
As for more thoughts on some stuff, I think Dissidia should stay most likely, it is a ton of fan service and well, most fans I know were pretty happy with it. I haven't got the chance to buy it yet personally. I know a version of Persona 3 is out/coming for the PSP, that should be on there since the game is already established to be quite good on the PS2 and the port is just adding more content. As for Persona 1 I think that goes back to the silly argument people were having before. It is made by Atlus who are well known for their RPGs and in particular the Persona series (especially around here) so a very updated remake of the original is something that should at least be worth "checking out" on this sort of list.

 
Million Ton Bara Bara is another one to keep your eyes on... 
 
  

What ever happened to Tekken 6?