I can't say that these PSP accessories are necessarily the best out there, since I haven't tried everything there is, but these are the things I actually use for my own PSPs. I've included all PSP models, since there are still lots of people using the older ones.
Sony Traveler Case (PSPgo)
Sony
Sony says it's durable and stylish, and while I haven't had mine long enough to really tell how durable it is, it does look pretty stylish. The PSPgo Traveler Case seems tough, anyway, and has a good feel in the hand. You're supposed to be able to fold it back and use it as a stand while watching video, but I couldn't quite get it to stand properly. Still, I'm pretty happy with this case--it's decent protection for your PSPgo for under $20.
PlayGear Pocket (PSP-1000)
I haven't seen the PlayGear Pocket for the slimmer version of the PSP (though I haven't really looked that hard), but I wouldn't do without it when taking my old PSP model on the road. Logitech's hard case is crystal clear but lined with black foam, and it perfectly cushions your PSP. I once dropped my PSP on a tile floor from around waist height and it was perfectly fine, thanks to the case it was in. It's even possible to customize the PlayGear Pocket--because it's clear, you can print out any design you like, cut it out, and insert it between the hard shell and the foam. A quick search on the web and you should even be able to find a Photoshop template all ready to add your own designs to.
System Skin Case (PSP-1000 and 2000)
Joytron's System Skin Case isn't really a skin or a case. It's more of a shell that fits snugly over your PSP. The one I use on my PSP-2000 is clear plastic, letting the silver of the PSP show through. It probably wouldn't be my first choice for protecting my PSP, but I put it on to review it and never took it off. It's thin enough that I mostly don't notice it's there, and it performs the manufacturer's stated functions--keeping fingerprints and scratches at bay--perfectly well. The System Skin Case it available for both PSP-1000 and PSP-2000 and comes in an assortment of colors.Pro Gear PSP Faceplate (PSP-1000)
CAMY
Installing one of CAMY's Dual Injection Pro Gear PSP Faceplates requires you to remove your original PSP faceplate, which voids your warranty, but since they're for the oldest PSP model, you're not likely to have a warranty left anyway. It really was only "a matter of minutes" to install, and CAMY thoughtfully includes a little screwdriver in the package. The designs are stylish (mine is the gold dragons), and the black background color works perfectly with the PSP design (it also comes in white).
invisibleShield (all models)
ShieldZone
ShieldZone is so confident in the durability of their invisibleShield that they've given it a warranty for forever. If at any time in the future the screen protector gets scratched, they'll replace it. It comes in two shapes for the PSP--one that covers just the screen and one that covers the whole front of the PSP. Mine covers the whole faceplate of my PSP-1000, and I pretty much don't notice it at all. Except there are fewer fingerprints on the front of my PSP, and no scratches on the screen.
Duel PSP Satchel (all models)
Everki
Everki makes two bags specifically for PSP, the Duel and the Force. I'd be hard pressed to pick a favorite (I own both) but I find myself reaching for the Duel more often, so it makes the list. The Duel is one of those super-comfortable 1-strap backpacks with a special padded pocket for your PSP and an assortment of other pockets for accessories. Both the Duel and the Force come in black, with your choice of dark blue or coppery orange front panel.
Siberia In:Ear Headphones (all models)
Icemat
When my cat chewed through the wires for my original PSP headphones I had to find a replacement. Now I use Icemat's Siberia phones for both my PSPs and my iPod. They're probably not the best earbuds out there, but they're pretty decent (though keep in mind that I'm a gamer, not an audiophile). They do a good job of keeping out most outside noise (except the really loud stuff), and they sound pretty good, whether it's music, games or movies you're listening to.
