My friend Aaron asked me for a list of PSP games that I thought he should check out.  Here is a quick list of what I think you should try out. 

1.  Crush - great puzzle platform game where you change the perspective of the camera from a side scrolling view to a top down view.  Definitely a mind bender towards the later levels but a great puzzle game that you can play on the go.  

2. Metal Slug Anthology - bullet hell classic from Neo Geo that has you battling through 6 different Metal Slug games in the series complete with unlockables.  The best part is that  you get infinite continues, and trust me you will need them - I almost ran out. 

3. Valkyria Crhonicles 2 - Turn based strategy of the next generation.  An alternate take on wars of the past where you take command of a band of troops consisting of snipers, lancers, scouts, and gunners. Customization is a strong point along with the beautiful cell shaded graphics. Portable strategy at its finest here.   

4. Final Fantasy Dissidia - Pit all the heroes, villains and everyone in between from the Final Fantasy series in an (almost) endless battle.  Each character has a variety of skills and this leads to a different playstyle for each of them.  A surprisingly strong 3d fighting game with competent battle mechanics from Square Enix. 

5. Half Minute Hero - The pinnacle of portable gaming.  Taking an epic RPG and condensing it down into 30 second chunks is genius, and they execute it very well.  Filled with humor and a variety of game styles, HMH is something that every PSP owner should own.  

Check out the video here: 

http://www.youtube.com/watch?v=0D7RVoXta2g