"There are products that go between the camera and flash and limit the flash trigger voltage -- these safety devices prevent damage to the camera when using a flash with a higher trigger voltage than the camera could otherwise handle."
To expand on this a bit....
Some modern cameras cannot tolerate the high trigger voltages of some older flashes. Too high a trigger voltage can destroy the electronic circuitry of the camera.
I do not know that the T3i's flash trigger voltage tolerance is... I do know Canon increased it in more recent models, but at one point their cameras weren't safe with any more than 6V. Try to find out what's safe for your camera.
But the Vivitar 2600 has a fairly high trigger voltage. It's been tested to 148V according to this website. The Vivitar 2600D isn't listed there, but reportedly has much lower trigger voltage, under 5V.
Before using a 2600 on a T3i I would want to know that camera's voltage tolerance. I wouldn't be very concerned if it were a 2600D.
If you have a Volt Meter, you can check the trigger voltage of your particular flash (there can be some variation, some older versions of Vivitar 283 measured as high as 600V). And even if the flash's trigger voltage is too high, or just to be safe, Tim is correct... there are devices that can be used, that go in between the flash and the camera, that limit the trigger voltage to protect the camera. One such device is the Wein Safe-Sync, that costs about $50.
I agree with Tim, that modern flash are so full featured and improved, it's almost not worth making do with old ones. All current Canon flash and all the discontinued "EX" models would be very useful on your camera. There are also som third party flashes that are reportedly pretty good (I haven't used them personally... I have several Canon 550EX and 580EX II that work great with all my EOS cameras.)