Are all camera lenses compatible with all SLR cameras?

For example can I put a Sigma or Nikon lens on a Canon SLR?
If not, how do I tell which ones are compatible with which camera?

No.

Here is how it would go with my camera:
I have a Canon EOS 550D. It has what is known APS-C sensor or more often called a 1.6x crop sensor.
With this type of sensor I can put on the following:
For Canon, EF and EF-S Lenses
For Sigma, DC and DG Lenses (With the Canon mount)
Nikon Lenses work on Canon too, albeit only with a special adapter.

Note Full-Frame DSLR cameras can't take EF-S or DC Lenses.

No, all camera lenses are not compatible with all SLR cameras. Each brand has slight difference. All lenses of a particular brand also not suitable for the same brand of SLR cameras. You should go through literature for compatibility.

The short answer is, 'no.' Camera lenses and their mounts are proprietary to each brand of camera. Canon, for example, has used their EF mount since 1986 while Nikon's F-mount has been around since 1959. The two are not interchangeable but, there are adapters which allow Nikon lenses to fit Canon cameras with some loss of functionality. That said, such adapters are rarely worth the expense and inconvenience that go with them. Sony and, Pentax each of their own proprietary lens mounts. Olympus, Panasonic and Samsung however, all share the same lens mount as part of the "Four-Thirds" consortium of manufacturers which includes Leica but, Leica doesn't make any cameras that use this lens mount.

Third party manufacturers like Sigma make versions of their lenses for each major camera mount. So for any given Sigma lens, there's a Nikon version, a Canon version, and in most cases Pentax and Sony/Minolta version as well. Again, you can't mount a Canon dedicated, Sigma lens on a Nikon camera body or vice versa. The same is true of Tamron and Tokina lenses.

For what it's worth, many years ago, Tamron made a series of lenses called "Adaptall" lenses which, with the use of adapters made by Tamron, could be made to fit multiple brands of cameras. These lenses were common in the late 1970s and early 1980s when most SLR camers were still fully manual and didn't "talk" with their lenses electronically to calculate exposure. In light of all the proprietary electronics and the differences in autofocus technology from one manufacturer to another, such lenses are not practical today.

Simple. Canon takes canon lenses and the Sigma (And tamron and tokina) lenses that say "for canon" on the box.