Rebeccah,

Suckers are not always bad. If the plant is grafted, with the desirable rose only coming from the bud union and above, then yes, they are always bad. If the plant is growing on its own roots, then the suckers are fine, within limits.

The limits have to do with roses which grow so aggressively that they sucker where you don't want them, eg into adjacent plants. This may happen with some Rugosas, Gallicas and Albas, for example. Others can add to this list of classes which tend to sucker. I have also noted it in some Explorer series roses.

Regina

Shoots of the desired variety coming from the base are called basals, and these are highly desirable. Shoots coming from below the graft (if any) are rootstock suckers. These have different foliage than the desired variety. Also, some non-grafted roses will make shoots from the roots some distance from the mother plant. These are also called suckers because they are not desirable. In other words, "sucker" is applied only to shoots you don't want, not to all shoots from the base.