I want to get a PSP, which one do I get?

A year ago, the answer to that would've been "A big old PSP-1000 (Fat) and a huge-ass memory stick". However, with the cracking of the PS3's Master Key (and thus the ability to sign things so that the PSP's stock firmware (AKA official firmware or OFW) can run it), things have changed. While technically only the PSP-1000 and certain 2000 (slim) models are fully hackable (able to flash a custom firmware (cfw) to the device proper), any PSP can run a "light" custom firmware like LME, and the only difference is you have to run it after booting up, instead of having it boot in to the firmware. As such, if you have no PSP right now, your best bets are the PSP-3000 (if you need to play UMD games) or the Go (if you don't).

Screenshot Title Genre Description
Bookr Bookr ebook reader Compatible with a wide variety of formats, including pdf, txt, palmdoc, djvu, chm, and html. Simple and easy to use.
Cavestorypsp Cave Story Action-Adventure Everybody's favorite indie game now on PSP!
Daedalusx64 Daedalusx64 Emulator Most of the games are still slow but for example Mario 64 works almost perfectly.
Doom PSP Doom, various FPS There are a variety of Doom ports, of varying quality and controls. Search around and find the one for you. I use PSP Doom Legacy, as the controls are wonderful, the graphics great, and support of lots of wads, but there's no music unless you add in each song as an mp3, which eats up lots of space so fuck that shit.
Exult PSP Exult RPG Lets you play Ultima 7 and Serpent's Isle on the PSP. If you don't know what Ultima 7 is and you claim to like RPG's, play it right now you fucking casual.
ScummVM PSP ScummVM Emulator Plays almost every 2D adventure game.
Kaiten Kaiten Patissier Puzzle Puzzlan gaems. You play as a girl collecting ingredients, and can spin the entire level 90 degrees at a time. There are 3 editions, each one increasing in difficulty from the last, but the music can get kind of grating and it's rather poorly ported, resulting in slower "turn" speeds and long loads for levels. Since it's a port, you can always check out the actual games on PC.

There's a few sequels if you can't get enough.

Lm3 Lamecraft Sandbox It's a free Minecraft clone on your PSP.
Masterboypsp MasterBoy Emulator A good Game Boy and Game Boy Color emulator that also includes support for Game Gear and Master System games.
SNES PSP Various SNES emulators Emulator Best over-all IMO is Snes9xTYL 4.2 ECM, but it's still not perfect, as Kirby Super Star doesn't work, thus making it useless to everyone forever. Alternatives include (Snes 9X) Euphoria, but it's somehow even slower despite being released later.
Tyrianshot OpenTyrianPSP Shoot 'em Up Everyone's favorite vertical shooter. If you don't know what this is you better try it now! Upgradable weapons, fully customizable ships, great level design and THE MUSIC! Originally made by the guys who made Jazz Jackrabbit and Unreal Tournament
OpenTTD PSP Open Transportation Tycoon Tycoon Sim Port of OpenTTD. Suffers from an entirely unfit for the tiny PSP screen size GUI, but it's not like you have many options for Tycoon games on the PSP. RCT2 when?
Picodrive PSP Picodrive Emulator An excellent Genesis / Mega Drive emulator with the option to play in US or PAL mode. Plays most if not all games, and even supports Sega CD.
Tempar PSP TempAR Cheat Plug-In It's a plug-in, so dont go lookin' for an eboot. It's an action replay for PSP games! Download cheat databases, or make your own cheats on the fly and feel like a super l33t haxxor.
Adom 6451 ToME Roguelike Port of ToME on the PSP. Controls are rather slow, but the whole game is here. In addition, Angband, Nethack, and Powder are all ported as well so get your roguelike on. If you're new to roguelikes, Powder is highly recommended as a starting game but it's no cakewalk.
Homers RIN PSP Homer's RIN Emulator Wonderful GB/GBC emulator. Even allows you emulate selecting different color palettes for GB games, like when you were a kid. Only caveat is that the controls default A/B to X/O. You can change 'em to Nintendo standard after, but still.

Another alternative is Masterboy, which defaults X/O to the proper keys, and is a similarly execllent emulator and probably surpasses Homer's RIN

Wagicpsp Wagic the Homebrew!? CCG Play Magic the Gathering on your PSP! For a homebrew effort it's pretty impressive, as there's rules enforcement and an AI, as well as thousands of cards. The controls are fast and intuitive, allowing players already familiar with Magic to pick it up in a few seconds.

Due to legal reasons, the game doesn't come with card images out of the box, but you can add them in yourself. Unfortunately, you may have to download card images one set at a time (slightly over a hundred files in total) and manually place them in the corresponding folders, since combined downloads may be hard to find, usually either leading to a dead link or in sone cases a malware infested site. Images also cause the in-game shop to lag horribly as you start you unlock more sets, but thankfully you can toggle images on/off from the options menu.

The game advertises support for custom campaigns but few have ever been released, and even those that have are buggy (frequent crashes, decks not shuffled, etc.) or won't function at all. Fortunately the main game offers tons of decks to face against and you can even play against your own deck.