General
Canon started the EOS line back in 1987 which replaced the FD and new FD (FDn) mount, making the FD lenses unusable to be used on the EOS line. Due to the change of the flange focal distance, the FD lenses would not be able to focus to infinity when using a mount adapter unless the adapter had a correctional element (glass). Canon did make an adapter with correctional glass that also had a crop factor of 1.2. Finding one of these adapters is nearly impossible as they were only available for professional photographers.
Canon EOS cameras are available in three mounts. The EF mount for full frame cameras, EF-S for APS-C cameras and EF-M for the mirrorless series.
The EF-M has a flange focal distance (FFD) of 18mm, same as the Sony E-mount. This implies that almost all vintage lenses can be adapted to be used on this type of camera.
The EF and EF-S mounts have a flange focal distance of 44mm. This makes adapting lenses of manufacturers with a FFD that is less than 44.5mm (considering 0.5mm for thickness of the adapter).
EF-S mount lenses can only be used on crop sensor bodies and not on full frame while EF can be used on both type of cameras.
Compatibility
Various adapters exist to make it possible to use FD(n), Minolta and other lenses which have a shorter FFD on a EOS body. These all have correctional glass that will always reduce the image quality. They will also have a slight crop factor.
Lenses with a mount that is larger than 44mm can be used with the help of a simple adapter. Most popular mounts are (Zenit) m39(x1), m42(x1), Nikon-F, Pentax-K, Contax C/Y, DKL mounts, Olympus OM and Leica R. A general misconception is that the FFD of the Zenit m39 and the most common m42 are identical. There is a minor difference of 0.26mm between the two.
Mount conversion
There are various sites on the internet that describe the change of the mount on lenses with a shorter FFD such as the Canon FD(n) range and the Minolta lenses. Among those are plans where the original mount is milled down or sanded down to reduce the FFD. These modifications are at your own risk if you would like to go that way. Modifications like this would also require you to have access to turning mills or other heavy equipment. It will also make the lens permanently modified.
It is also possible to get modifications like this done without damaging the lens. The Lens Doctor in the UK does modifications on some FD lenses, but at the time of writing it is unsure if he is still in business. EdMika, based in Canada, creates conversion kits that enable the end user to completely replace the mount and aperture mechanism of Canon FD(n) and some Minolta lenses, keeping the original parts untouched.