Genetics are interesting and spontaneous mutations happen all the time. Most are insignificant (such as in a non-coding region of DNA), immediately lethal to the cell or, at least in mammals, killed off by the host immune system.

Random mutation can be seen in roses. The mutated shoot is often called a "sport". If you know how to graft, you can then propagate the new variety. In fact, more than one rose variety commonly sold in nurseries was originally propagated from a mutated shoot.