In Vancouver where I live there is a lot of products out there which repair or at least say they repair a asphalt roof. The truth of the matter is that if you have more than one hole in the roof there is a common issue all around that is causing this problem to exists. It might be age, animals or the weather. It could even be the construction of the house or the lack of ventilation.
What ever the issue it is best to figure out what caused the leak before you replace with a new roof or even repair so that you are not going back and forth repairing new holes chancing a problem that is not going to fix itself. If one hole appears in the shingle it is a sure bet that many more are on their way. If one or two holes a appear and that is all then you are dealing with a incorrect labour installation and this will be resolved right after the repair is made.
The only real repair product for asphalt is asphalt. It is sold in a liquid form mixed with a rubber Palomar to help the repair remain flexible. beware when layering this asphalt that it is not seeping under the shingle and getting absorbed into the deck. You should have a underlay but might not if you roof is leaking, therefore beware about adding to much of the repair goop you purchase.
Most cases though are in need of a total replacement, there are not many roofing repair companies in the city I live in for this particular reason