Is it possible to transfer cancer to someone else?

No: Cancer itself is not contagious. More recent understanding of some cancers has lead to our understanding that certain viruses cause some cancers to develop. Specifically, most cervical cancers and many head and neck cancers are related to hpv and the recent vaccine should greatly decrease these diseases in the future. Nasopharyngeal cancer is associated with ebv. Most people already have hpv.

Very very rarely: The only time I have seen this is during organ transplantion when the donor had an unknown cancer that then appeared in the recipient. These are case reports and extraordinarly rare. So in a nutshell to answer your question from a practical standpoint i would say no.