Ok... this is the same problem that I run into every year, which makes me start considering the move over to C++ (which I always talk myself out of in the end). I just want to find a decent physics engine to start using so I don't have to make my own. I really like Slick's Phys2D port/package, which is great for 2D stuff, but doesn't help me with 3D movement and collision response. I looked up ODEJava, but their main site appears to be down, and last I heard their binaries aren't updated for the newer (Intel) Mac platforms (which is why I'd like a native Java library if possible).

Could someone please point me in the right direction? 

Bullseye! That's what I was looking for. Thanks! 

There are also:

https://jmephysics.dev.java.net
http://joode.sourceforge.net
http://www.jphysx.com

Does anyone have experience with these? Joode looks dead and it's been some times since there was activity at jphysx.

I had looked at all of those already, and for the most part, they're all dead projects (or so it appears anyway from their releases). JBullet is the most active, and it's the only "pure java" solution I found.

So has anyone tried JBullet and can talk about the quality of it? I'm especially interested in how it integrates collision detection coming from my code and in how physically stable it is (whether or not things oscillate in certain circumstances, how it handles slowdowns etc).

I have implemented a pure Java port of the ODE engine, it's available here www.ode4j.org.
The current beta is fairly stable (only two issues with the GL rendering in the demos), the engine itself has no known problems.
The main missing feature is a trimesh support, which I'm currently working on.