What kind of space object tracking software is there out there?

There are several flavors of space object tracking software available on the internet - some free and others that cost some money. If you are looking for software that will show an object's position (RA and Dec) in the sky, there are numerous planetarium programs that do that. There are also programs that give a "space view" of the solar system from anywhere in the solar system. Here are a few sites worth checking out that may be of help:

The Minor Planet Center 
Near Earth Objects Dynamics Site 
JPL Horizons

Also, search the web for "astronomy software" for more information on programs that are available.