Do digital SLRs like the Canon Rebel series have a shutter?

It uses a focal plane shutter - just like its 35mm ancestors.

While cheaper cameras certainly just turn on the sensor to shoot (diverting power from the screen to do so, hence the lag), DSLRs still use the proven shutters that have served pros and amateurs alike for generations.

There is an actual shutter on this camera- it is mechanical. Cameras have had shutters since the 1880's at least. Prior to that cameras did not have shutters = the photographer removed the lens cap and let the light in for a fixed amount of time. Photographic materials were not as sensitive to light as what is now available so a shutter wasn't all that necessary. With the invention of film in 1885, built in mechanical shutters became necessary on most cameras. Pinhole cameras are the exception: many of them are still built without mechanical shutters, but the more expensive ones do have a shutter. The CMOS cameras have mechanical shutters, CCD can have electronic shutters. These would be expensive.

If it's a CMOS sensor, it has a mechanical shutter.

If it's a CCD sensor, it may have an electronic shutter.

Generally, electronic shutters allow flash sync speeds 1/400 seconds, or faster. Sync speed on a mechanical shutter is around 1/200 to 1/250 seconds.

Almost every camera has a shutter to control the time period to let the light fall on the sensor or the film. If there was no shutter, it wouldn't be possible to take photos with correct exposure. In good light, photos would be washed out and in dark, photos would be too dark if there was no control to let the shutter open for shorter or longer time period.

All DSLR cameras - Sony, Pentax, Olympus, Nikon and Canon - have a shutter that blocks light from reaching the sensor until you press the shutter release.

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