NO. I'll assume you're asking about modern lenses & will explain. Canon lenses that can auto focus come in 2 mounts. EF & EF-S.
EF mount lenses fit both full frame bodies & crop body cameras (Rebel series, 10D thru 70D & 7D)
Lenses specifically designed for crop bodies ONLY use an EF-S mount due to the concept that the sensor is considerably smaller & therefore the light path through the lens can also be smaller. This allows building smaller & lighter lenses for the crop bodies.
Much older lenses didn't have internal electronics & used another mount.
No, crop sensor cameras (all Rebel cameras, 40/50/60D, and the 7D) can take EF or EF-S lenses. Full frame cameras (all 1D, 5D and 6D) only take EF lenses.
The mirrorless camera (EOS-M) use EF-M lenses, but can use EF and EF-S with an adapter.
You posted to a rather old thread, but...
The 5D III has a "full frame" sensor and uses Canon EOS "EF" lenses (it can also use all of the specialty lenses such as the TS-E, MP-E).
The 5D III cannot use EF-S or EF-M lenses -- nor is there any adapter that would let you use them (you wouldn't want to even if such an adapter existed.)
The "S" in EF-S stands for "short" back-focus.
A lens projects a round "image circle" into the camera which not only completely covers the area occupied by the sensor, but also spills off a bit on the sides (the lens is round even though the sensor is rectangular). That diameter of that image circle needs to be larger than the diagonal measure of the sensor size.
All EF lenses project an image which is large enough to completely cover a full-frame sensor which measure 36mm x 24mm and has a diagonal measure of just slightly more than 43mm. But a camera with an APS-C crop frame sensor measures about 22mm x 15mm and has a diagonal of just under 27mm. So the EF lens is projecting a much larger image than necessary (the diamter of the image circle is 16mm larger than it needs to be.)
Canon designed the EF-S lenses to project images which are just large enough to cover the size of the APS-C sensor, and by doing this everything can be smaller and the back-focus distance can be shorter and the complete design reduces the expense of the lens and means they can offer you that lens for less money than you'd have to pay for an EF lens of the same focal length.
ALSO... since the angle of view will be a little narrower when using an APS-C camera at any given focal length (as compared to a full-frame camera's angle of view) the ranges for a typical working zoom lens would be more versatile if the entire focal length were shifted a bit shorter. This is why you can find a working zoom for a full-frame camera such as the EF 24-70mm and yet a working zoom for a crop-frame camera is typically 18-55mm (such as the EF-S 18-55mm f/3.5-5.6 IS STM).
The EF-S lenses have the identical mounting coupling -- even the pin-outs for the lens control are identical. The difference is that the rear-most element on the lens protrudes back so far that it actually projects slightly into the camera body. This is a problem for a full-frame body.
On a crop-frame body, the sensor is smaller and that means the reflex mirror can also be smaller and needs less space to swing clear of the light path when you take a photo. So there's room for that rear lens element to protrude slightly into the camera body.
On a full-frame body, the sensor is physically larger and that means the mirror needs to be larger and it needs more room to swing up when you take a photo. If a lens element was protruding into the camera body, the mirror would hit that lens element and result in damage.
To keep this from happening, Canon designed a bit of a lip on the full-frame bodies which is not there on crop-frame bodies. If you attempt to mount an EF-S lens on a full-frame body, the rear element will hit that lip and you'll notice you can't even get the lens to seat on the mounting flange.
The bottom line is... even if it would fit, you would not be happy with the images (which would be black at the edges and corners.)
Older manual focus Canon FD and FL lenses cannot be used on newer Canon EOS cameras either. FD and FL lenses date from the 1960s through the early 1990. There are adapters available, but Canon's older mount lenses are generally are only marginally usable on the later mount cameras, if at all.
Previous posts are correct:
The current Canon EF lens mounting system for EOS cameras was first introduced in 1987. It incorporates electronic contacts to operate the autofocus and control the aperture in the lens. This type lens is usable on all EOS cameras, including film and all formats of digital sensors.
Canon EF-S lenses are a variation of that mount, only usable on the APS-C crop sensor cameras beginning with the Digital Rebel (300D) in 2003. These are special lenses designed to complement these smaller sensor cameras, including all the Rebel (xxxD and xxxxD) line, 20D through 70D, and 7D. These lenses will not fit 10D, D60 and D30 or any of the earlier DCS digital or EOS film cameras. Nor can they be fitted to 5D series, 6D or any 1D series models.
So, in other words... APS-C cameras, which are the bulk of the DSLRs that Canon offers, can use virtually all modern lenses: both EF and EF-S. Meanwhile, full frame and APS-H size sensor cameras are a bit more limited, to EF lenses only.
There are also many third party lenses made in the EF mount. Some of these are full frame capable (i.e., usable on all Canon cameras). Others are "crop only", designed for use on the APS-C sensor size cameras only. The "crop only" lenses use the same EF mount, but if put on a FF camera, they will vignette strongly.
Incidentally, a good deal of other manufacturers' vintage manual focus lenses can easily be adapted for use on modern EOS cameras. It's possible to use old Nikon, Pentax, Olympus, Leica R and other lenses, via some simple adapters. Of course they remain manual focus only, and the aperture is also manually controlled. More info on adapted vintage lenses here.
Finally, just within the past year or so a couple EF-M lenses have been introduced, which are another variation on the EF mount. These are designed for and only usable on the mirrorless EOS-M model (so far).
07/31/2023: New firmware updates are available.
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04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM