Suddenly it seems that there's a lot more to orbital resonance than just the Lagrange points I learned about it school:

Paul Wiegert's Web Page: ...I'm interested in the dynamics of the Solar System, particularly its smaller bodies, asteroids and comets. I'm also interested in the dynamics of planets in extra-solar systems around other stars, and in celestial mechanics in general.

The Earth companion asteroid 3753 Cruithne: I have been involved in an a study, in collaboration with Kim Innanen (York) and Seppo Mikkola (Turku), of near-Earth asteroids. During this research, we discovered that the Earth has a companion asteroid. If you would like to know more about asteroid 3753 Cruithne, you can visit its home page here.

Asteroid 2002 AA29: Quasi-satellite to horseshoe and back again.... Most near-Earth asteroids have no consistent dynamical connection to our planet. However, those that go around the Sun in precisely the same amount of time as our planet fall into 1:1 mean-motion resonance with our planet (which just means that both go around the Sun once in the same average (mean) amount of time). These rare bodies are called Earth coorbital or companion asteroids; they in some sense share the Earth's orbit with it. With a highly circular orbit that is the most Earth-like seen so far, and able to transit between two distinct types of resonant motion, is the newly-discovered ECA 2002 AA29.