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

• Field Commander
• Gran Turismo
• Grand Theft Auto Chinatown Wars (the best GTA)
• Hellboy The Science of Evil
• Jackass The Game
• Killzone Liberation
• Metal Gear Solid Portable Ops & Peace Walker
• Midnight Club LA Remix
• Motorstorm Arctic Edge
• Socom Fireteam Bravo 1-3
• Star Wars Battlefront Renegade Squadron
• Twisted Metal Head On
• Untold Legends Brotherhood of the Blade
• Worms Open Warfare 2
• Ys Seven

Patapon 2

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).

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).

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 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 played Lumines so much I would see squares when I closed my eyes

Crisis Core Dissidia Locoroco Lumines

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

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.

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.

Honestly, besides nostalgia value, the games really aren't that good because there's only one analogue stick. But back in the day my most memorable, enjoyed games were GTA, Daxter, and Persuit Force.

Untold legends: brotherhood of the blade…. And the unfinished elder scrolls oblivion

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

PATA PATA PATA PON!

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

Final Fantasy Tactics: War of the Lions

Arguably the best way to experience the game.

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.

Work Time Fun

Valkyria Chronicles 2 and 3 are PSP exclusives, if you liked the first one on PC or PS3 (I think the 3rd game needs a fan translation patch though).

There's a couple decent Jak & Daxter exclusives, too.

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

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

Final Fantasy Dissidia duo decim and Crisis Core were the only games I really enjoyed on the PSP.

Locoroco. It was just so sweet and cheerful.

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.

Jeanne D'Arc

A fantastic RPG.

Original games - LocoRoco Midnight Carnival, Crisis Core Final Fantasy VII, Daxter, Trails in the Sky trilogy, LittleBigPlanet PSP, Silent Hill Origins, MGS Peace Walker, Gran Turismo... Remasters/ports: SMT Persona 2 Innocent Sin, Lunar SSSC, Breath of Fire III, Tales of Eternia (all of these games are JRPG, and all of them are the best version of these games in my opinion), Crazy Taxi, Prince of Persia games, Tomb Raider games...

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

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.

@PeculiarGoat Lumines was one of my faves,even though I got it as a pack-in.

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.