In 1960, the rhesus monkey kidney cells used to prepare the poliovirus vaccines were determined to be infected with the simian virus-40 (SV40),[36] which was also discovered in 1960 and is a naturally occurring virus that infects monkeys. In 1961, SV40 was found to cause tumors in rodents.[37] More recently, the virus was found in certain forms of cancer in humans, for instance brain and bone tumors, pleural and peritoneal mesothelioma, and some types of non-Hodgkin lymphoma.[38][39] However, SV40 has not been determined to cause these cancers.[40]
SV40 was found to be present in stocks of the injected form of the IPV in use between 1955 and 1963.[36] It is not found in the OPV form.[36] Over 98 million Americans received one or more doses of polio vaccine between 1955 and 1963 when a proportion of vaccine was contaminated with SV40; an estimated 10–30 million Americans may have received a dose of vaccine contaminated with SV40.[36] Later analysis suggested that vaccines produced by the former Soviet bloc countries until 1980, and used in the USSR, China, Japan, and several African countries, may have been contaminated, meaning hundreds of millions more may have been exposed to SV40.[41]
See: side effects section.
"In 1998, the National Cancer Institute undertook a large study, using cancer case information from the institute's SEER database. The published findings from the study revealed no increased incidence of cancer in persons who may have received vaccine containing SV40."
And beyond that, a full discussion requires comparison of negative side effects of the vaccine vs side effects of the original virus, and the rate of such effects. We know, factually, that there are often some side effects from vaccines. We also know, factually, that often the vaccine side effects are either of less severity and/or less frequency than the effects of catching the original virus. In other words, statistically, most of the time you're better off tempting fate with the vaccine than with the virus.
The closest thing was the lingering concern about SV40-contaminated doses (importantly, not the actual vaccine itself) causing increased rates of cancer, although it looks like all major attempts to determine if that was true have so far come back with a null result.