A sport is a genetic mutation within a rose plant. It results in a branch that's much taller than usual (a climbing sport) or a branch that produces yellow instead of pink flowers (a color sport) or a branch with blooms made up of double or single petals instead of the very full shape of the mother's blooms or visa versa.
Hybrid Teas are known for sporting quite easily. Many HT's have climbing sports ; Mme Caroline Testout for example got a climbing sport and this sport is now much more popular than the original bush form. Other examples are Étoile de Hollande climbing or Crimson glory climbing, Lady Sylvia climbing etc...
Old roses did get especially color sports and sports with a different flower shape.
The chance of getting a sport is 1 in 500.000 or even 1 in a million. Ann Boudolf from Lens Roses in Belgium told me that she only saw three new sports during more than 30 years and they created hundreds of thousands roses over the years so seeing a sport in your own garden is unlikely but it happened in my garden of all places...
When Park Abbey rose was created my husband and I had three of them growing in pots in our garden and this to evaluate the rose. When the first blooms emerged everything was normal with the expected salmon pink old fashioned blooms. Suddenly I noticed that one rose had a branch with rather yellow buds. Great excitement of course but we had to wait until the bud was fully opened to be sure. Two days later the bud unfolded into a glorious golden yellow old fashioned bloom. The shape and fragrance identical to the parent but a totally different color. We took the branch to Lens and they used it to graft the yellow sport. Today she's growing in our garden to evaluate her before bringing her on the market. But why does she need to be evaluated first?
Well, sometimes sports aren't as viable as their parent plants. They can be weaker and start to deteriorate quickly so it's not good to bring such a weak rose onto the market, how beautiful she may be.
Some sports also have the inclination of sporting back to the mother plant. This means that the bush starts to grow new wood with the same flowers as the mother plant. Also this isn't a good feature, we need to make sure the sport is stable.
I already mentioned the climbing HT sports but here are some other very famous sports:
Mme Ernest Calvat, Light pink sport of Mme Isaac Pereire
Mme Pierre Oger, Very light pink sport of La reine Victoria
Baron Girod de l'Ain, white lined sport of Eugène Fürst
Capitaine Dyel de Graville, deep pink sport of Souvenir de la Malmaison
Souvenir de St Anne's, double sport of Souvenir de la Malmaison with also stronger fragrance
Augustine Guinoisseau, Almost white sport of La France
Souvenir de St Anne's, sport of Malmaison
Mme Pierre Oger, sport of La reine Victoria
Chippendale climbing, sport of Chippendale
Baron Girod de l'Ain, sport of Eugène Fürst
Capitaine dyel de Graville, mauve pink sport of Malmaison
Mme Ernest Calvat, lighter pink sport of Mme Isaac Pereire
Yellow Park Abbey rose, sport of Park Abbey rose
Park Abbey rose with her yellow sport on the same plant