Have you had access to all the seventh-gen multi-plats, or were you a Nintendo-only gamer? Just curious, because it opens up a lot more games if you didn't own one of the HD twins/a capable PC.
Regardless, my recommendations are:
- Ratchet & Clank: A Crack in Time (you can also buy the HD Collection & Tools of Destruction).
Third person shooter-platformer hybrid that bucks the "over the shoulder" view and borrows a few ideas from Super Mario Galaxy.
- LittleBigPlanet 2 (consider the first game as well if you want an enjoyable single-player experience)
2D platform game meets "platform for games". Community levels will keep you occupied for months, level creator can keep you occupied for years.
- WipEout HD Fury
Futuristic racer that packs in just about every game mode you can think of, making it my personal favourite PS3 racing experience.
- Infamous (second game is also worth picking up)
Open world superhero game featuring one of the most entertaining stories this gen. Play good or play bad. Definitely worth picking up.
- Heavenly Sword
Beautiful hack 'n' slash adventure. Not worth full price, but very much worth picking up for the price it's going for pre-owned.
- Valkyria Chronicles
Incredibly enjoyable strategy-rpg, probably one of my favourite games to come out of Japan this gen.
- Metal Gear Solid 4 (you can also buy the HD Collection & the original game on PSN. I wouldn't start with 4)
Ending to a story I'd been following since the late 90's. Beautiful, heartbreaking and a thoroughly fantastic journey.
- Portal 2
Absolutely stellar first person puzzle game. An incredible experience; surprisingly great co-op mode as well.