Is the Canon EOS 60D hot shoe the same as the Canon EOS T3i's hot shoe? I want to know if I can use any Canon EOS camera to fire a strobe. The strobe works with EOS 60D.
It's the same. The 60D and T3i both came out around roughly the same time and their pop-up flashes and hotshoe have the exact same capabilities. Any strobe that works with and doesn't fry a 60D will work with (and not fry) a T3i.
The Canon hotshoe, physically, has been relatively unchanged even from film days. How the electronic communication is interpreted by the camera occasionally gets updated, but is generally backwards compatible. But there may be some compatibility issues if you use a very old flash or a very old camera (i.e., film-era).
Older hotshoe flashes can have very high sync voltages. And the current generation of Canon dSLRs, while rated to withstand 250V on the hotshoe, may still not be enough to guarantee not being fried, since some vintage flashes have been measured with sync voltages in excess of 300V. And if you're using a first-generation Canon dSLR (D30, D60, 10D, and 300D) those cameras' hotshoes were only limited to 6V. Most digital-era flashes (like the Canon EX models) are usually within this limit, but some might still be higher.
In addition to this, Canon's TTL scheme changed for digital. Putting a digital-era flash on a Canon film dSLR won't cause any issues--it can switch automatically from eTTL-II to A-TTL. But using a much older flash on a digital camera can mean your TTL metering will be off (or may not fire--see comments below), since the flash won't speak eTTL. You should still be able to use manual mode (if the flash has it). And (if the flash is pre-TTL old) auto-thyristors don't depend on flash/body communication and still work just fine.
If we're talking manual studio strobes used via PC cable, or manual radio or optical triggers, there shouldn't be any issues--manual only triggering is non-brand specific and should work across any ISO-compatible hotshoe.