Kate's motivation for coming back to the island was finding Claire.

Sun's motivation was finding Jin.

Sayid wanted no part of coming back.

Jack's motivation was that he felt it was his destiny.

Hurley's motivation for coming back is not yet clear.

Ben's motivation for coming is not yet clear, but
I think we will discover it when he gets judged on Wednesday

None of them came back to save the Left Behinds. This has not become a huge issue yet, but I do not think that they are going to be able to work together until this has been dealt with.

I think that it is going to take Locke the savior to knock some sense into them,show all of them that they were chosen to be on the island for a reason.

I'm going to disagree with you on Kate and Jack.

Kate said she was going to find Claire, but to me that feels like a big load of BS.
I think her real motivation was running away from life again. She couldn't handle the buttoned-down life of raising Aaron, having to be responsible for a child, keeping "the lie" going, etc. She just runs away from any and every problem that comes up in her life. Her character is one of the few on the show who hasn't evolved in the slightest bit.

Jack on the other hand, I feel went back out of guilt. As far as he knows, Locke committed suicide. He is riddled with guilt over this for not believing in Locke, and he was truly duped into believing that his going back to the island would fix something and make up for it. As we know, jack is a fixer, it's what drives him.

I still don't think the O5 having to return really has anything to do with saving the Lefties. Aside from possibly avoiding The Purge (which they probably could have done on their own since they already knew about it), they didn't really need saving.
I think this was just a big load of BS cooked up to convince them to go back more easily. Although I'm not sure why Ms Hawking would help perpetuate Ben's lie, although she has obviously manipulated people in the past to serve someone's purposes (like with Desmond), although who or what's purposes is yet to be seen...

I think Hurley's motivation was probably to save the Left Behinders... but I do agree on many of the other points...

I don't think Kate insistence on finding Claire is BS... she does want to find Claire for Aaron's sake... although she has no idea how and because of that, it seems as if she is just there... plus now she's in the 70's which doesn't help matters. I think she also went back for Sawyer... which if they get back to 2008 might have Kate and Sawyer on a dual quest looking for Claire... or gold... or both?

I think Jack went back to save the others and yes, fix things, but he never considered that they didn't need or want to be saved. That's part of why Jack is acting so passive... he doesn't really know why he's there.

We can only postulate that Ben's coming back had something to do with the war in which Widmore hinted. But you're right that we might soon discover Ben's intentions...

Locke came back 'cause Jack brought him.

Frank came back because he was the pilot on 316.

Hurley came back to give someone that guitar he was clinging to on the plane. I'm guessing Charlie asked him to bring it to him. Why else would he agree to go when he was so adament about not going before? His bud asked him to. Where is the guitar by the way?