Mike, yes your 35mm Canon lenses should fit/work on a digital Canon. As a general rule most lenses are backwards compatible and should be okay. But I'm not 100% sure about retention of AF facility on Canons. Suggest you check with a dealer/Canon for avoidance of doubt.
Owing to the fact that the sensor on a digital SLR is smaller than a single piece of 35mm film your lenses will, however, produce a rather different field of view. The conversion factor is tied in to the size of the camera's sensor. The absence of an industry 'standard' sensor size means that the conversion factor varies slightly from one make of digital SLR to another. In the case of Canon it's 1.6x.
Siimply multiply the focal length of the lens you intend using by the conversion factor to give you its angle of view, were it being used on a 35mm film camera. Since 35mm film cameras have been around for a while most photographers are more familiar with the approximate angle of view that 35mm lenses cover. A 28mm lens on a 35mm camera is a moderately wide angle lens, but when used on a dSLR with a smaller-than-35mm sensor size, its angle of view becomes smaller. Multiplication factors on Nikon, Pentax, and Minolta cameras are 1.5, Canon, 1.6, and Olympus 2.0. So an 18mm lens (18 x 1.5 = 27) on the first three takes in the same angle of view as a 27mm lens on a 35mm camera. On a Canon, it would be 29mm, and on an Olympus, 36mm.
So, stick your 70-300mm lens on a digital Canon and it effectively becomes the equivalent of a 35mm 112-480 lens, and the 28-105 to 45-168. Not a problem if you shoot portraits, wildlife or sports but it can be more restrictive if you like to use wide-angle lenses for landscapes or photojournalism.
Lenses made specifically for digital cameras are usually smaller and lighter and are designed to cover the area of the smaller sensor. In other words, if you used them on a 35mm film camera, the image would be vignetted i.e. darker in the corners. They are also are designed to bend light rays so they hit the sensor more or less straight on which, manufacturers claim, results in a better image. But in reality the consensus seems to be that 35mm film lenses can produce equally good results because they cover a much larger area than the sensor and use only the centre of the lens - the so-called "sweet spot" - to produce images. The fact that they often have larger maximum apertures than digital lenses can also be beneficial.
James