Ratchet & Clank: Size Matters.

Played through that sucker more times than I care to admit to.

The only game that others haven't mentioned but I think you should definitely check out is Ace Combat X (never mind Joint Assault though).

Yeah, Monster Hunter Freedom Unite was probably also the game I spent most time on my PSP.

It depends on what games you like, but I loved Persona 3 Portable and Kingdom Hearts Birth by Sleep.
If you liked Monster Hunter, you could also try God Eater. It is a really gold Monster Hunter Like with a good story!

Jeanne D'Arc

A fantastic RPG.

No one ever talks about it, but Ratatouille game on psp was really fun, seemed superior to the home console versions in terms of fun

There are plenty of good titles already mentioned here so I'll go with something less popular.

• PangYa: Fantasy Golf - it's a golf game, as you can guess from the title. It has simple but really fun gameplay with customisable characters (outfits and equipment, the latter affects character stats). It also has a story mode to get you started.
• Puzzle Quest - RPG with match 3 gameplay for combat. Really addictive in a "just one more quest" kind of way.
• Ridge Racer 2 - it's Ridge Racer. Riiiiiidge Racer! Tons of content, bunch of modes, fun to control - it's great! Might be my favourite handheld racing game (and definitely one I spent the most time with). It's pretty much a celebration of the franchise until that point, especially the classic era.

Crisis Core Dissidia Locoroco Lumines

And the vast catalog of PS1 games you could download from the PSN store.

I never owned a PSP, but tried a few in an emulator. Really missed out on a fantastic device and game library. I think there are some obvious famous games that many recommend, as such

• Crisis Core: Final Fantasy 7
• God of War - Ghost of Sparta
• Grand Theft Auto Liberty/Vice City Stories
• Lumines
• Metal Gear Acid / Peace Walker / Portable Ops Plus
• Monser Hunger Freedom Unite
• Persona 2 Innocent Sin
• Ratchet and Clank Size Matters

Also kind of ports I think, maybe new games in series, I'm not sure. But just able to play these on a portable device is awesome:

• Gran Turisomo
• Littlle Big Planet
• MotorStorm: Arctic Edge
• OutRun 2006 - Coast 2 Coast
• Tekken 6

I didn't play much on PSP yet. Following are also interesting:

• Ghost in the Shell Stand Alone Complex
• Hot Shots Golf
• Jeanne d'Arc
• R-Type Command
• Tekken - Dark Resurrection
• Ultimate Ghosts 'n Goblins
• WipEout Pure

And the list goes on and on. This was an awesome handheld.

MHFU is definitely my favorite too. very fond memories as I'd get together with my friends (who had moved away) once or twice a year to do the big hunts we struggled with on our own.

I also really liked star wars battlefront: (rogue squadron?). was a bit shit to aim with no second stick but I remember the incinerator plus a lock-on killed anything real quick.

My favorite is when I go pspspspspsp to my dog and he comes over for cuddles.

No but really, if we're talking full exclusives, Ridge Racers 2 is pretty much all the good stuff about the old RR series but with better graphics and most of the content from all games. If we're talking non exclusives (sometimes the best version though), Final Fantasy IV, Castlevania Dracula X Chronicles, Final Fantasy Tactics WoTL, and Tactics Ogre, Let US Cling Together are pretty top tier

Rengoku 2, I wish there was a modern game that could expand on the gameplay of it.

Neopets rpg

wipEout, Jeanne d'arc, Battlefront, locorocco, peace walker, Ys seven, Mega Man Powered Up, Gran Turismo, Dissida, Final Fantasy Tactics, Ghosts of Sparta

Disgaea: Hour of Darkness

Lumines! All of them. I might go home and see if my PSP or Vita still hold a charge (and I can find the games).

I really loved playing the racing games on it. -Ridge Racers -Gran Turismo -Street Supremacy (Tokyo Xtreme Racers) -Initial D: Street Stage

Final Fantasy Tactics: War of the Lions

Arguably the best way to experience the game.

I just miss game sharing. Multiplayer games across 2 PSP's with only one copy of the game was so peak. Tekken specifically I guess to answer the question

I got a PSP exclusively to play Kingdom Hearts: Birth by Sleep. Would not recommend lol

Thexdar. I thought it was even better than the DOS version.

I got Wipeout Pure so I could do the browser exploit wayyyy back in the day. I ended up really enjoying the game too!

If you're into racing games, you could try ‘Colin McRae Rally 2005’ — it's quite good and even requires a bit of knowledge about racing setups.

‘Race Driver 2006’ is also alright, it's an expanded port of ‘TOCA Race Driver 2’ with lots of content and okay physics.

There's ‘Twisted Metal: Head-On’, which is reportedly pretty good and in the vein of the first two games in the series (which had a different feel from 3-4 and probably ‘Black’ too).

If you're into making music, check out LittleGPTracker: it's a tracker-style app that works on PSP among other platforms and allegedly can load samples, as a tracker should. Inspired by the famous LSDJ for the Gameboy.

Monster Hunter 3rd with English patch is incredible! I got all my friends’ PSPs modded when the fan translation came out and we all played together, it was mindblowing!

Otherwise DJ Max Portable is 99% of my PSP and Vita time. DJMP2 is the best of them.

PixelJunk Monsters Deluxe & Everyday Shooter are amazing games from small indie studios.

LittleBigPlanet, Ratchet and Clank and Daxter are some must plays from Sony.

GTA Vice City Stories, MGS Peace Walker, Star Wars Battlefront Renegade Squadron are fun games from third parties.

Honourable mention for The Sims 2, not for being good. But for being interesting

Aw man, this reminds me that I have a busted PSP I need to fix. I've been wanting a pocket emulator for some time, and I used to have a PSP ages ago that I'd jailbroken to play SNES games lol

God of War: Chains of Olympus. I got pretty good at the sex minigame.

ModNation Racing is basically Sony's version of Mario Kart and I remember it being pretty fun. The characters and cars are customizable.

LittleBigPlanet was pretty reduced in size for the PSP version, but I still had a great time with it.

Crush and ff tactics remake stood out to me but there were a bunch of great games on there wipeout, monster hunter, persona 3, etc. Crush is a 2d/3d puzzler with a really interesting soundtrack and ff tactics the story and characters and soundtrack hold up well.

Yeah, for me it’s The 3rd Birthday, Jeanne D’Arc, Lumines, and Tactics Ogre. All of them are straight bangers.

Work Time Fun

People have mentioned a lot of good ones, so I'll just mention ones I haven't seen listed.

• Wipeout Pulse is also really fun and should be checked out
• Rock band Unplugged
• Mercury meltdown
• Blast Off
• Disgaea (if you have a hundred hours to spare grinding)
• Everybody's Golf 2
• Hot shots tennis
• Grand theft auto China town Wars
• Mega man powered Up
• Pixel junk monsters deluxe
• Patapon
• Space invaders extreme
• Tony Hawks underground 2 remix
• Half minute hero (I never played this but it's on my list as the next one I want to play)
• Daxter

tomb raider legend has an awful framerate but then puzzles are fun, patapon is addictive, crisis core ff7 is a gem! ridge racer is also a fave

Death Jr. 1&2

Work Time Fun

I think every single favorite of mine is listed already so I will list the niche one I don't see:

Gundam vs Gundam Next Plus

Space Invaders Pocket! One of the more complete Space Invaders collections.

...Also Space Invaders Extreme, although the DS version is preferable.

There's a really nice port of Dariusburst, too. And N+ is always a good time on any system.