Suckers

Most modern roses sold are actually two roses in one - the variety you want on top (ie. Peace, Double Delight, Iceberg, etc) grafted to root-stalk (most commonly Dr. Huey). Most roses sold begin life as a bud-eye grafted onto root-stalk, which enables commercial growers to reproduce roses in large quantities in the growing fields. Though roses grafted onto vigorous root-stalk quickly develop, sometimes the root-stalk is so vigorous that it sends up sprouts from the roots. These root sprouts are called "suckers" because if left on the plant they will overtake the rose, sucking all the energy into growing more root-stalk rather than the roses you want.

Unsuspecting gardeners will sometimes proudly point to the red double flowers that have suddenly appeared on long slender stems from their rosebush, thinking they've got something special. Dr. Huey may look pretty, but given the choice between growing beautiful blooms of "Double Delight" or a mass of suckers, I think most would prefer the rose the former!

The easiest way to identify suckers is to look for the source. They key is to check out the bud union, the big knotted place where roses are grafted to the root-stalk. On grafted roses, canes that grow from the BUD UNION OR ABOVE is good v.s. canes that come from BELOW THE BUD UNION are suckers. Below the bud union means the trunk or roots. It helps to plant roses in mild climates with the bud union a couple of inches above the soil level, makes it easy to check at a glance. Otherwise you might have to dig around a bit to check where the growth is coming from. A word of caution, do not make the mistake to think canes coming from the bud union itself (whether the top part or bottom) are suckers, those are BASAL canes which are very good new growth.

The best way to remove suckers is to pull them off clean. Cutting suckers off generally leaves a bit behind which can re-sprout, so try to remove as much of the sucker as possible.

Unless a rose is sold/purchased "grown on its own roots" the rose is grafted to root-stalk. Rose that are grown on their own roots (typically old garden roses and miniatures) never have suckers because the entire plant is the same rose variety. Alas most modern roses are grafted to root-stalk, so learn how to identify and deal with suckers so you're not one.