Would any camera lense work on my t3i?
Say if I buy a Nikon camera lense for my canon will it work?
No.
You need to buy a lens with a Canon EF mount, it doesn't have to be a lens made by Canon, there are third party lens manufacturers like Sigma, Tokina, Tamron etc, but you need to make sure the lens has the proper mount. Nikon do not make any lenses with Canon EF mounts, and Canon do not make any Nikon mount lenses.
You need a Canon fit EF mount for this camera - many to choose from, new and old.
Always good to visit a store and try out a lens, get a feel for it before you buy. All lenses are not created equal! - for canon try to stick to L series lenses.
No. All camera manufacturers use a proprietary lens mount and there's no compatibility between brands with the exception of Olympus and Panasonic who share the Micro 4/3 lens mount. So if you own a Canon T3i buy Canon lenses for it or buy Sigma or Tamron lenses with a Canon mount.
No. You need an EF or EF-S mount lens.
Nikon has the longest lens mount to sensor distance of any current DSLR camera (46.5mm), Canon EOS mount uses a lens flange to sensor (or film) distance of 44mm, the older FD and FL mounts used 42mm, so there's room for the mechanics in an adapter the get the lens to physically fit.
Canon have another quirk in that they need to 'see' a lens before they will release the shutter so adapter manufacturers install chips to fool the camera into thinking that there's an EOS lens fitted.
You will, of course, lose auto focus and you can only use Nikon lenses that have an aperture ring, but they will meter correctly.
As the camera can no longer control the aperture you can only use Aperture Priority as the only Auto Mode and Manual.
So the answer is - yes you can, but why would you want to, unless you have a load of known good Nikon lenses?
The system that is best for for using old lenses, and has a purpose behind it, is the Micro 4/3 system, with a lens flange of only 19.5mm you can use all kinds of exotic glass, Angenieux, Leica, Zeiss, Bolex, Canon lenses made for TV cameras (how does a 12 - 100mm f1.2 sound to you?) pretty much any lens ever made. In case you don't know Angenieux made most of the lenses used in Hollywood and are still around.
http://www.angenieux.com/
No.
You need a lens with a Canon EF or EF-S mount.
You can get adapters to use Nikon lenses and some others, but you won't get autofocus or auto-aperture, and will have to shoot manually.
edit: "Chris" wrote:
"Canon have another quirk in that they need to 'see' a lens before they will release the shutter so adapter manufacturers install chips to fool the camera into thinking that there's an EOS lens fitted."
Sorry, Chris, that's completely wrong. You can fire a Canon DSLR shutter with no lens attached at all, with a simple t-mount attachment, and with dozens of lens/thread adapters. I use my various Canon DSLR models with older Pentax screw-thread lenses regularly (no chip in the adapter at all), and to do astrophotography with the camera attached to a telescope, no chips.