I eschewed the advice to get a Wii rather than a PSP, for various personal reasons. (Such as the fact that I'm a graduate student living in a hovel with a tiny TV and very, very little room)
My preliminary (one-week) impression is this: the PSP is good now. After playing Gradius collection and Capcom classics, I'm fully convinced that this is the system for classic 2D compilations. I don't think the d-pad is as horrible as some made it out to be; it's no worse than a standard Playstation D-pad, and just takes some getting used to.
I must say, I've been enjoying SOCOM: Fireteam Bravo and Metal Gear PO quite a bit, as a fan of FPS's and stealth games. I especially enjoy Metal Gear Online; while some might claim it's merely "Metal Gear Quake", I think it breathes new life into generic online deathmatch. There are also some interesting RPG and strategy influences on the single player play of Metal Gear, as well.
Another nicity is that the games seem to be fairly cheap now, much more than DS games. For instance, I saw Street Fighter Alpha 3 for $15 at Circuit City the other day, and some of the games I have (such as SOCOM, Lumines, and Gradius) are only $20.
Anyway, for those of you who have been sitting on the fence for the last two years over whether to get one: the PSP is good now. There's probably a price drop on the horizon next, which I should have maybe held out for. Oh well.
I think most of the bad-mouthing of the PSP is from ex-Sony fanboys who stood in line ten hours to buy one, and then realized there were no games besides Lumines. (which I honestly haven't had time to play yet...)
I don't think the PSP will supplant the DS, but I think it's certainly the Gamegear of today, to say the least.