I only need collision. If you could point me in the right direction (like AABB or so?) I'd be happy.
Well, unless you want to write your own physics engine (do not, and I mean DO NOT do this), you have to use physics engines. That is pretty much what they are for, if you aren't using something like aabb. I would just use JBullet and be done with it.
No, see, just using a physics engine because you can, is doing it wrong. Yes physics engines have collision checks but its a small part.
Do not use a physics engine just because you need collision checks.
Actually there are many many many many cases in which having a physics engine as opposed to just collision algorithm would make everything harder to code.
most games have "physics", HOWEVER physics engines are mostly for games that want to replicate REAL physics(realistic games) or it is the main focus to play around with physics(angry birds)
we do SAT is one of our games
all of these OBB, AABB, rects, spheres or whatever work just fine without a grid
how often and when you do collision checks is important from the performance point of view
like having a grid and only check collisions among them, then do sphere checks first and only if thats true too, do real collision checks - something like that