This is an extremely difficult question and one I've considered before. I absolutely refuse to give you an outright answer but will do my best...
Infamous - I originally bought my first PS3 in the summer of 09. I bought it to play PS3 exclusives such as Disgaea 3 but was a pretty hardcore 360 user. I checked out the Store and downloaded some demos. One of them was Infamous. I loved it. The next morning I went and bought the game. I couldn't stop playing. The open world combined with the powers and story, good vs evil. I loved every second of it. While it's not my favorite PS3 game of all time, it was a catalyst for me eventually switching to the PS3 as my Primary Console and eventually selling my 360, switching to the PS3 exclusively.
Ratchet & Clank Future: A Crack in Time - This is the most fun and interesting game I've played. It was my first exposure to Ratchet & Clank and I loved every second of it on my way to Platinum. I can't recommend this game enough to anyone who owns a PS3 and sits firmly in my list of 'Must Haves' for a PS3 owner.
Demon's Souls - This could quite possibly be the true 'Favorite PS3 Game' for me, if I were to take the time to agonize over who actually gets the Top Spot. The exploration combined with the tenseness of what awaits around the corner combined with the PVP from Invasions, which scratched and itch I've had since the Ultima Online days, made this a truly unique and amazing experience. Add to that the depth of both Character and World Tendencies (how do they think up this stuff?) and you have yourself a gem.
Uncharted 2 - Do I even need to go into details here? A friend had urged me to get this and in prep for it I bought Drake's Fortune and got the Plat. I immediately pre-ordered 2 and the rest is history. It was an amazing and engrossing ride all the way through the game with plenty of laughs and thrills and that train ride.. wow!
I could go on with many other titles but will leave it with the 4 listed and depart with the comment of "The PS3 has so many awesome games, especially in the Exclusives Department, that I am extremely glad I decided to try the console out. It has become the center of my Home Entertainment."