suggest the best and defining titles on the platform

Off the top of my head...I liked all of these...Killzone: Liberation, Little Big Planet, Socom Fire Team Bravo 3, MGS: Peace Walker, Hot Shots Golf, Burnout: Legends.

MGS peace walker IGN gave it a 10 i think (must be good if IGNorant gives it a 10)

umm what elese..final fantasy 7 crysis core is apparently good,

GTA vice city storys and liberty city storys and chinatown

god of war: ghost of sparta and chains of olympus

LBP

gran turismo

kingdom hearts birth buy sleep

ratchet and clank: size matters

secret agent clank

valkyria cronicles 2

resistance: retribution

killzone: liberation

and if ur a huge FF fan you can get final fantasy 1 and 2 on psp

GT, God of War, LBP, GTA:CW, MGS, Lumines, FF7:CC,Killzone.

My experience with the PSP is limited, but if you'll tell me what kinds of games you like, I might know a few games that you'd enjoy.

What geners do you like ?

Well here is a few personal favorites  (in no particular order)

MGS Peace Walker

Syphon Filter: Logan's Shadow

God of War: Ghost of Sparta

Ace Combat X: Skies of Deception

SOCOM: Tactical Strike

Resistance: Retribution

Dead Head Fred

Patapon

If you like JRPGs

YS Seven

Kingdom Hearts: Birth by Sleep

Jeanne d'Arc

Crisis Core: Final Fantasy VII

Disgaea: Afternoon of Darkness

Tactics Ogre: Let Us Cling Together

Valkyria Chronicles II

Final Fantasy Tactics: The War of the Lions

guys above have mentioned a lot of great games, I'll try and add few more to it

Daxter

Resistance: Retribution

Dead Head Fred

Wipeout: Pulse

Patapon

Persona 3 Portable

Tekken (Dark ressurection is a classic!)

Burnout:Legends

FF: Dissidia (Duodecim is coming out end of the month)

Exit (simple puzzler, I thought it was very enjoybale and underrated)

Monster hunter Freedom Unite.

Well if you ever plan to get an NGP you should get your titles on PSN, though you'll pay more than the games are worth and have to buy memory cards, and not have the best game on the system since it's not on PSN.

If not the first game you should get is Kingdom Hearts, after that games like MGS Peace Walker, Portable Ops, the entire Monster Hunter series, Little Big Planet, Resistance, Crisis Core, Tactics Ogre, and some of the PS1 games that were ported to the PSP like Ape Escape and Final Fantasy Tactics.

There's a number of other titles I could suggest but those are the best titles that will likely also last the longest.

Tactics Ogre: Let Us Cling Together

the main reason i bought a PSP.

but the 2 God of War games are also phenominal! although i have yet to pick up Ghost of Sparta.