I am going to buy a nice new 10" Craftsman table saw to replace the old hand-me-down from my father in law, but all of the dado blade sets I see are smaller (7 or 8"). Will I be able to use these blades with the new saw I am looking at buying?
In short, as long as the diameter of the arbor on the stacked dado blade set matches the arbor diameter of your table saw or radial-arm saw, the answer is yes.
There are actually a couple of reasons why you don't need an 10-inch dado blade set. Since dadoes rarely need to be cut deeper than about an inch-and-a-half, an 8-inch dado blade set will be large enough to cut the necessary dadoes and rabbets.
Additionally, by making the dado blade set only 8-inches in diameter, there is less weight to the blade set, which lightens the amount of effort that the saw must put forth to cut a wide, deep dado. Of course, it stands to reason that the smaller diameter blade set would likely cost a little less than a 10-inch set (since there's less steel needed to build the blades and chippers).
When buying a stacked dado blade set, be sure that you purchase a set with the correct arbor size for your saw. Most modern table saws and radial arm saws have a 5/8-inch arbor onto which the blade will fit. However, there are a few rare instances where a saw (or blade set) doesn't have a 5/8-inch arbor. Trying to use a blade with too large of an arbor hole simply can't be balanced properly for use. Conversely, if your blade set has an arbor hole too small for your arbor, resist the temptation to drill out the arbor, as you may not only put the blade out of balance, but the heat from drilling may alter the temper of the blade.
I have had instances where the paint in the arbor hole of a dado set made the blade very difficult to install onto the arbor. In this instance, if you choose to take a rounded file to the arbor, take off only the paint from the arbor hole, once again, to avoid putting the blade out of balance.