In reply to David Hooper:
You can get basecamp here
http://www.garmin.com/garmin/cms/us/onthetrail/basecamp If you have mapping on your edge thn you can see it in basecamp without having to install the maps on your computer.
Track is generally a recording of what you have done. i.e. the track you actually followed, rather than the route you planned. Can contain thousands of points. Route is a pre planned set of (way)points that you navigate point to point. A route gnerally is limited in the number of points it can have, which is why Garmin invented courses. A course is also a set of pre planned points that you follow, except you can have special icons for hills, or water / food stops, or turn directions etc. A course can also have thousands of points so is very good for long or complexs rides you are planning.
tcx and crs are just different Garmin file formats. TCX can contain courses, track or routes or all three. A CRS can only contain courses and is a smaller file size. GPX is a universal GPS file exchange format compatible across virtually all GPS. Your EDGe will record the track in GPX format.
Training centre is the older software and hasn't been developed since they started Garmin Connect (which followed the motion based site). A beta for Training centre came out last month but it is looking dated. I use training centre because thats all there was when I got my edge 305 aeons ago, and it also stores the data on you computer. I use Garmin connect occassionally if I want to share a ride I'm planning or hav done.
Good websites to checkout
BikeRoute Toaster
GPSies
Open Street Map and Open Bike Map
Look out for the open source software Golden Cheetah - very good.