***Update***
I've completed the game....Yeah....already. While it was a great experience from start to finish, I wasn't expecting it to be this short. I believe my total played time was just under 4 hours. Totally a rental, IMO.
One word: WOW
This game is amazing. I had some time to play it this morning (stupid insomnia) and was blown away by the quality of many aspects. First thing you're going to notice are the graphics. They are PS2 quality, or better; and considering that this is running on the PSP, this is an amazing feat. I've played God Of War 1 before, and it was pretty good. I was never totally astounded by it, but I did like it. I never got around to playing GoW 2, but rest assured I'll be trying it after I finish Chains of Olympus.
God of War games are unique in that they start you off sprinting and you never slow down. They throw you right into the action from the moment you put the disk in. All in all, God of War games are very cinematic. Not to be read "they have a lot of cinematics." Rather, the story progression and the way it is told throughout the game is a cinematic experience.
Keeping with this cinematic experience, the music is fitting as well. It sounds like it was taken out of a blockbuster movie, and the musical direction is superb. Battle music is invigorating and exciting, and depending on your locale the ambient music is always a fit.
Boss battles are fun and challenging, and lets not forget the gore. You can't have a God of War game without tons of blood and brutal executions. I mean, at your very first boss encounter you take out a giant Basilisk's eye by smashing it with a battering ram, dropped by an ogre who was bitten in half by the Basilisk. Later on in the level you finish him off by pulling two stone towers on to his head, then jump on his head and break his jaw. All of this is in the first level.
I've progressed the story a bit further and am now tasked with returning Helios, the Sun God back to the skies. I look forward to continuing to play, and highly recommend you check this game out.