The US servers are staying open so companies are still releasing games on them. XSeed and Gaijinworks still have at least 4 games left that're planned to be released on the US PSN store.
For digital-only psp games, there's a few that might be interesting depending on your tastes:
Brandish (not out yet)
Trails in the Sky SC (not out yet)
Corpse Party
Unchained Blades
Black Rock Shooter
LocoRoco Midnight Carnival
No Heroes Allowed
Patchwork Heroes
I've only played a few PSP...
PSP 2000, hackable version (there are non-hackable 2000's so be careful of that).
The 3000s can only use lite cfw, and the GO doesn't support UMDs (plus even though the screen is nice it's smaller, and the controls are a bit more cramped too)
fyi, PSN will still work for anyone in the US, its just being taken down for everywhere else:
http://www.ign.com/articles/2014/09/10/sony-to-cut-playstation-store-access-for-playstation-portable-in-several-regions
Bumping this to let anyone who doesn't know that this games pre-sales are going on right now and they end tomorrow. If you don't get one before then you'll be out of luck unless you're willing to pay ebay scalpers.
http://www.gaijinworks.com/GW_presale_reg.htm
Four ways:
1. RemoteJoyLite - Video quality is terrible and your frame rate will be much worse for most games.
2. Emulation via JPCSP or PPSSPP - Poor compatibility and tons of glitches for most games that do work, requires a fast PC, but games can be run at a high resolution.
3. LKV7000...