1. Asteroids that cross Earth's orbit: These are called Earth-crossing asteroids, or Near-Earth Objects (NEOs). Some examples include:

* Apollo asteroids: Cross Earth's orbit from the outside.

* Aten asteroids: Cross Earth's orbit from the inside.

* Amor asteroids: Come close to Earth's orbit but don't cross it.

2. Asteroids that orbit a particular planet: This is a bit trickier, as asteroids don't really "orbit" planets in the same way that moons do. However, some asteroids have orbital paths that are influenced by a particular planet's gravity. These asteroids are often described as being in a "resonance" with that planet.

Examples of asteroids in resonances with planets:

* Trojan asteroids: These asteroids share Jupiter's orbit, clustered around the Lagrangian points 60 degrees ahead and behind Jupiter.

* Hilda asteroids: These asteroids have a 3:2 orbital resonance with Jupiter, meaning they complete three orbits around the Sun for every two orbits Jupiter completes.

It's important to note that there are many other asteroids with unique orbital characteristics, and these are just a few examples.

If you're interested in learning more about specific asteroids, you can search for them online or use databases like the Minor Planet Center (MPC) which contains detailed information about asteroids and other small bodies in our solar system.