The Canon extenders are physically compatible with all prime (fixed focus) Canon EF lenses with a focal length of 135mm or longer except for the 135mm 2.8 SF. They are also compatible with a handful of recent L series zoom lenses. The full official list is:

70-200mm 2.8L
70-200mm 2.8L IS
70-200mm 4L
100-400mm 4.5-5.6L
400mm 4 DO
135mm 2L
180mm 3.5L Macro
200mm 1.8L
200mm 2.8L
300mm 2.8L IS
300mm 4L
300mm 4L IS
400mm 2.8L IS
400mm 5.6L
500mm 4L IS
600mm 4L IS
1200mm f/5.6L
Consult Canon when checking out newer L series lenses introduced since this list was written, and you’re on your own if you use third party lenses. You can also use Canon extenders with Canon TS (tilt-shift) lenses, but it should be noted that the TS lenses can’t report to the camera that the extenders are there.

Autofocus is not supported by non-pro EOS cameras when the 1.4x converter is used with 100-400mm 5.6L, 400mm 5.6L, 500mm 4.5L, 1200mm 5.6L, and with the 180mm 3.5 Macro when it’s focussed closer than 0.8 metres, or when the 2x converter is used with the 70-200mm 4L, 100-400mm 4.5-5.6L, 180mm 3.5L Macro, 300mm 4L IS, 300mm 4L, 400mm 4 DO, 400mm 5.6L, 500mm 4L, 500mm 4.5L, 600mm 4L, and the 1200mm 5.6L.

Note that there are two generations of the Canon Extenders - the original 1.4x and 2x models and the mark II successors, which add improved weatherproofing. The 1.4x II is said to be optically identical to its predecessor but the 2x II has minor optical enhancements.