Carcinogenic is a scary word, but what exactly does it mean? The International Agency for Research on Cancer (IARC),  a part of the World Health Organization (WHO), has established a framework. The IACR reviews scientific evidence for and against carcinogenicity claims and places agents in one of the following categories:

• Group 1 – carcinogenic: Sufficient evidence exists that an agent is carcinogenic in humans. In this group we find, as expected, agents like various forms of radiation (gamma, x-ray, utraviolet), tobacco smoke, alcohol, estrogen-progestogen oral contraceptives, and asbestos.
• Group 2A – probably carcinogenic: Strong evidence exists that an agent is carcinogenic, yet the evidence rmains insufficient to be sure. More precisely, there is sufficient evidence of carcinogenicity in animals but limited evidence in humans. This group contains, for example, acrylamide and occupational exposure to oxidized bitumens and their emissions during roofing.
• Group 2B – possibly carcinogenic: Some evidence exists for carcinogenicity of an agent, but it is neither sufficient nor strong. This class comprises agents like chloroform, coffee, DDT, marine diesel fuel, gasoline and gasoline engine exhaust, and certain surgical implants and other foreign bodies.
• Group 3 – unclassifiable: Evidence is inadequate; the agent may or may not be carcinogenic, we do not know enough to tell. This category contains agents like caffeine, carbon-nanotubes, static or extemely low-frequency electric fields, fluorescent lighting, phenol, polyvinyl chloride, and rock wool.
• Group 4 – probably not: We have evidence that an agent is not carcinogenic. Perhaps due to publication bias, this group contains only one element, caprolactam.

The IACR publishes classification criteria and lists (by category, alphabetical). Wikipedia also maintains lists by these categories with links to the respective pages.

Keep in mind that this classification represents only the state of evidence regarding cancerogenicity in humans, not your risk of becoming exposed to an agent, a dose-response assessment, or overall health risk from exposure. Hint: everything that kills you quickly and reliably is unlikely to cause you cancer.