Box2D

What do you like best?

It is a high performance 2D physics engine, great for creating impressive looking games or tech demos.

What do you dislike?

The learning curve can be pretty steep for a beginner. You'll need to brush up on basic physics terminology and vector math. Sometimes the code required to create physics objects can get a little verbose.

Recommendations to others considering the product:

If you're looking for just a 2D physics engine, then chances are you'll give Box2D a try and love it. If you want features found in a game engine like rendering sprites, user input, etc.. this is not for you.

What problems are you solving with the product? What benefits have you realized?

Box2d allows you to create impressive games or tech demos with interesting mechanics. It's a ton of fun to see images on the screen come to life and behave realistically. The performance is also better than many other 2D physics engines available. It has bindings for many different languages so you can use whatever language you are most comfortable with.

The only downside for me is that there isn't an official javascript version to be used on the web (aside from a few 3rd party versions that may or may not be up to date with the official version.