If I find a random dollar and I didn't see someone drop it or no one's around that could have dropped it, then hey, it's mine. But if I find say, a sack FULL of money, it's going to the police. It could have been stolen. I wouldn't know. It's just the right thing, too. Don't know where it came from or where it was going.
Items though...it's weird. If I found something like Triforce did, I know I'd be absolutely distraught to lose my bag with my games and such in it, and that being said, I'd take it to wherever I could so that it could hopefully be returned. I'd probably look for a name or something in the bag first though, cause like Triforce said, you don't know if they will actually return it. I guess the more expensive or personal (like a blanket or stuffed animal) it seems, the more likely I am to try to return it. But if it's something random, possibly junky, I would either keep it or leave it, depending on my interest. lol
And of course, lost pets should always be returned home, unless it was a bad one. Though some pets don't have collars, so that makes it hard. If there's no collar, I probably wouldn't think anything of it, unless it was a nice breed of dog that you just know didn't come off the streets. Put up signs and stuff around the neighborhood and hey, if no one comes to claim it in a certain amount of time with correct proof, then I've got myself a new fuzzy friend!
Basically I don't wanna keep anything I know someone would need or miss terribly. I wouldn't want to lose something and someone keep my items, but judging by some replies, I'm glad I'm extra cautious with my favorite stuff haha.