Pros: Quick load times. Stunning graphics. A full GTA gaming experience on a handheld.
Cons: Lack of licensed music. Suffers some control and camera faults similar to previous GTA games.
The bottom line: Far and away the best PSP game yet. It's essentially just GTA3 with new missions and on a heldheld, but that in and of itself is an amazing accomplishment.
This game was one of the reasons I purchased the PSP when it first came out. The game was originally scheduled to be released just a few weeks after the system was released here in North America but it didn't release until 10/25/2005.

I've had this game for 2 days now and this review is being written with the intent of dispelling some of the mis-information that has been written in reviews elsewhere concerning this game- many of those reviews complain about load times and controls and were written well before this game was ever released. That leads me to believe that many of those reviews were written based on speculation and not from actual hands on experiences.

Background on the game:
It's set in Liberty City and uses the same map as GTA3 but it's actually a prequel to GTA3 with totally new missions. You play as Toni Cipriani who had a minor role in GTA3.

NOTE that the game does force you to upgrade your PSP to version 2.0 of the PSP operating system if you haven't done so already. The upgrade is included on the game's UMD and should only take a couple of minutes provided that you have a fully charged PSP (the PSP will not allow you to perform the upgrade if your PSP is not charged at least 50% regardless of whether or not you have it plugged in).

The positives:
-The game plays and looks a lot like GTA3 did on the PS2. It's amazing to me that they were able to fit as much of the game as they did onto a UMD. The various cars, pedestrians, weather and night and day effects, and seemingly open environment that made GTA3 seem so amazing when it first came out on the PS2 are all there on the PSP.
-I was especially surprised at the number of radio stations that the game has- I thought for sure that would be one thing that would be sacrificed in order to make the game fit on a UMD.
-I found the controls to be easy to pick up on and similar to the controls of the GTA games on the PS2.
-The load times are quick- much quicker than the load times on any of the GTA PS2 games and quicker than the majority of other PSP titles. I've been through about 10 missions so far and the load times occur in between missions and last around 5 to 15 seconds depending on the mission.

Some of the negatives I've encountered so far:
-The cars can often be difficult to drive and are prone to spinning out uncontrollably at times. It's not so bad as to make it unplayable, but still can be annoying.
-Rockstar didn't invest in the rights to music like they did with Vice City and San Andreas. There are a few very obscure licensed songs, but the majority of the music is similar to the music used in GTA3- original compositions that sound like popular music from the time period but are not truly authentic or very good. The games makes up for this somewhat by allowing you to play MP3s from your memory card as a custom radio station (a feature which I'm surprised hasn't been adopted by other games- would have loved to have seen that option in Burnout Legends) but by playing your own music you miss the DJ banter and the awesome commercial parodies. NOTE: The feature to play your own music has to be unlocked in one of the missions- it's not there at the start of the game.
-The game stutters very briefly (maybe a half second) sometimes when switching radio stations.
-The camera angle goes crazy on a few occassions making it difficult to see what you're doing- but that was a problem with all of the GTA PS2 games too.
-Some of the missions are extremely short. I believe this was intentional because this game is designed for a handheld gaming device and as you make it further into the game some of the missions do get longer. But still, a few of the initial missions take less than a minute to complete.

Overall:
I'm extremely impressed with the game. It's definitely not without faults and nothing about it seems to be a revolutionary advancement of the series like Vice City and San Andreas seemed to be when they came out, but it's amazing what they were able to accomplish by fitting what they have onto a UMD.
If you're expecting GTA3 for the PSP that's pretty much what you get.
I'm only about 10 missions into the game (out of supposedly about 70 total- not including about a dozen side missions) and I think with even my limited time with it so far I can safely say that it's easily the best most detailed game for the PSP so far.

NOTE: This game- like all of the GTA games- is not intended for children. It contains strong language and violence and is rated M for Mature.