The biggest reason to leave shingles in place before applying a second layer is a reduction in cost and effort required for the new roof. This also eliminates the need to dispose of the old shingles, which would require a truck or trailer not often available to a home do-it-yourselfer. The down side is that sometime in the future both layers of shingles will need to be removed before the next roofing project.
But It's Heavier
A roof can only carry so much weight without structural damage. If you have the added weight of two layers of shingles, the amount of capacity available to carry a snow load is reduced. This is only an issue in areas where heavy roof loads occur naturally.
Second Layer Shingling
The second shingle should be the same length as the old shingle. This allows the shingle to lay flat on top of the old shingle without creating hollow spaces that could easily be punctured by hail. Use nails about a half inch longer than normal in order to pass through the old layer of shingles and have adequate penetration into the wood of the roof.
Making the Decision
Remove shingles if they are breaking or curled. Void spaces in the old shingles could create hollows under the second layer. Expect a shingle roof to last up to 25 years depending on weather and circumstances. Check the south side of the home, the area that receives the most sunlight, for signs of damage. Also, check the roof boards for decay. If the wood below the shingles needs repair, the only option is to remove the shingles for access.