Well, yes and no.
The 360 version had trophies, but the PS3 version doesn't. And the things awarded by trophies just aren't interesting enough to do without a reward (collecting flags hidden around the world, killing templars).
The game works by giving you an assassination mission and you need to investigate your target, to both find out information about his whereabouts/habits as well as the crimes he is committing. Then you get to assassinate him and you need to escape.
You only need to complete 3 investigations per assassination, but you can do them all if you'd like.
So you can speed through the game or take your time. But besides that, there's not much else to do, no.
The latter two games are WAY superior. Like, in every possible way. I'd still say play AC1, though, before you plat AC2.
And AC1 is still a great platformer.