Before we get to the list, it is useful to understand that, frequently, roses that make lots of flowers descend from multiflora hybrids and fragrance is a rare bonus. Furthermore, multiflora hybrids tend to make relatively small flowers. The upshot of this is that, generally speaking, one can choose either lots of floral color or fragrance: usually one cannot get lots of flowers and fragrance. The nominal exception to this rule crops up in the hybrid musks, so named because many of them get fragrance from another side of the family. Even in this class though, the most foliferous rose is Ballerina who has no fragrance. The more fragrant of the hybrid musks tend to be a bit less well covered with flowers. Polyanthas are, in general, well furnished with flowers; but it is a very rare polyantha that smells good.
This list starts out in order; the first five or ten roses are, on average, better than most of the rest of the list. But after that there is just some random fluctuation from entry to entry. How one experiences the rose will depend on a host of environmental and cultural variables. Furthermore, there may be a number of ramblers or other roses that are not very highly popular that belong on this list; but most of these are pretty durable and vigorous where they are cold hardy.
Roses appear to do whites and pinks best. There are some good red shows, but when it comes to bright yellow and orange, it is generally pushing the envelope a bit. This said, we have listed a few in these color regions. They may not be quite so foliferous as some whites and pinks that are not on the list, but sometimes some variety is called for.