As a JRPG fan, and a fan of the anime art style, there are several exclusives for the PS3 that I've loved. First is Disgaea 3, I loved the first two and the third is extremely enjoyable, goofy SRPG with lots of leveling and extremely high replay value (if you have to patience to go through hours of leveling even after the final fight. Second would be Hyperdimension Neptunia, extremely cultish (read if you don't like JRPGs don't even try) but to fans like me the game centered humor, the story centered around Sony, Sega, Nintendo, and Microsoft duking it out while faced with the impending doom of pirate software and social gaming is great.
There are several more "JRPG style games" like Ar Tonelico and Trinity Souls that I like as well, all PS3 exclusives. As for different genres you should already know about the many exclusive triple A titles like Little Big Planet and Killzone, both great series in my opinion. I've never had a problem with playing online when the system is up, with a good internet connection little big planet and Metal Gear Solid 4 are great fun online (although I'm 95% a single player gamer).
As for the system, having a lithium battery makes recharging the controllers easy, fast, and long lasting. Being able to change the harddrive easily is also a factor (upped my 60 gig to a 500gig, the great PS1 classics and games like Agarest War over the PSN fill up a drive fast). I never noticed much of a different in loading between my PS3 and Xbox 360, so even though the blu-rays can hold more they don't take long to load from.
Overall the PS3 has been my favorite system of this generation, I love my Xbox 360 but I can't say there are many games that I'll remember in a year. With the PS3 I still have games that I fish out of my pile and get excited over, which really makes a system for me.
A few more games that I loved:
Altelier Rorona
Valkyria Chronicles
Eternal Sonata (the PS3 version had the option of original voices, makes a difference to me)
Star Ocean 4 (same as above, nice to have the Japanese style layout as well)
There are several more games coming out later that I'm interested in as well, like Disgaea 4 and Catherine. Sure I'm into cult games, but that makes the PS3 my favorite system.