The Canon Rebel or EOS XXXXD Series
Beginner/Intermediate models for hobby photographers who are transitioning to dSLR's, and looking to start, but within a moderate budget. The difference between the different Rebel cameras you've listed are just subsequent upgrades, and features: more megapixels, HD video, faster burst rate, etc. These camera's are quite capable of producing amazing pictures. What they lack in comparison to the higher priced line-ups are typically features and options. Much like you would expect when going from a base-model car to it's fancier deluxe model. These camera's use an APS-C sensor, which results in a 1.6x Field of View crop when compared to a 35mm film negative. A 100mm lens when used with an APS-C camera will result in a Field of View that is equivalent to 160mm on a 35mm film camera. These bodies make for excellent choices if you are on a budget, new to photography, or not sure how deep you want to get into the world of SLR photography (you aint seen nothing yet, alice).

The Canon 60D or XXD Series
This is what has been dubbed the prosumer model. Taking all the features of the Rebel series and adding many more options, to create a camera that suits well for a beginner, but enough features and options that advanced photographers can make use of, resulting in a body that will "grow" with you as you advance in your skills. These camera's have a more advanced AF system compared to the Rebel series, have a high burst shot count, making them suitable for action photography, but lack in many of the features found in Canon's pro line. These camera's make for excellent bodies for someone who has experience with SLR photography, or new comer who is serious about getting into photography. For many pro's, these bodies serve as a 3rd body backup (some even using them as 2nd body backups). These bodies are also APS-C bodies, so any lens paired with the body will have a 1.6 FOV crop.

The Canon 5D Mark II/5D Mark III
This is Canon's non-professional line Full Frame camera. Unlike the Rebel and XXD series, the 5D Mark II and 5D Mark III have a full frame image sensor. Thus there is no Field of View Crop. They are designed for studio and landscape work, primarily because of the slower burst rate, and AF system. These are more specialized bodies; they are a step up in terms of both features, and image quality from the XXD line, but lack in the high-speed performance that the XXD offers for sports.

The Canon 6D
The 6D is Canon's newest and least expensive DSLR sporting a full frame sensor. Unlike the 5D Mark III, the 6D has a cropped viewfinder, allowing the photographer to see only 97% of the frame before shooting. Notable features include built-in WiFi, GPS, HD video, and build quality similar to that of the 5D and 7D.

The Canon 7D
What The 5D Mark II is for studio and landscape photography, the 7D is for sports, wildlife and action shots. This is a specialized camera with an AF system, and high burst rate designed to offer sports/action shooters a lot more performance. The 7D is an APS-C 1.6x crop camera, like the Rebel and XXD series.

The Canon 1 Series
This is Canon's professional camera line. These are built with the tough demands of professionals in mind. I have seen hobbyist shooters with 1 series bodies (and certainly if money was no object I would have a closet full of 'em). It sports an insane AF system, a tank-like build quality, and a fine degree of control and features that allow users to custom tailor the body for their needs. The bodies are full weather sealed, when paired with a weathersealed lens. The shutters have a very high life expectancy, and it's very common to see used 1 series bodies with shutter actuation counts in the 200,000 range. Canon has two types of 1 Series bodies, each specialized for specific needs:
The Canon 1D Series is designed for the sports/action/wildlife shooter with a very high burst rate, and a highly sensitive AF system tuned to keep the focus on the action. This body is a 1.3x crop factor.
The Canon 1Ds Series is a full framed body ideal for studio and landscape work. It has a very high megapixel count, and has tonal range suitable for studio work.

Now, that isn't to say you can't use the 1Ds for sports, or the 1D for studio work. Either will work, just that the 1D has more features specific to action, compared to the 1Ds.

That also goes to say that you couldn't be a professional photographer using Rebel bodies. All these camera's, when used properly, are capable of producing AMAZING images. It's more that the Canon 1 Series is designed to be used abused in a daily basis, where as the Rebel is not.