Multiple bodies and/or backs, with flash. I always have a flash on at weddings, just because it makes one at least somewhat adaptable to most situations. Though I usually do not use it, it comes in handy when the film happens to be too slow for a shot that is worth taking. You can shoot it into the ceiling to add some light, and it won't stick out as being all that different from the ones shot in ambient light. However, after shooting one or two weddings, you generally know when to have your camera loaded with what (which is why the flash is used so little).
If you have to, just rewind a roll and change films, or finish off the roll quickly.
With digital, I like to have three bodies for shooting candids at a wedding, though the third is just a convenience, to prevent changing lenses as often. I shoot plenty often and just fine with two. With film, I like to have at least two on me, and two or more bodies (or backs) loaded with a different film, just in case. However, the times when I shoot film at weddings are few and far between. When I do, it is usually medium format, and the shots are of the more formal variety. You are correct that digital has great advantages in this area.