Taxanes - Taxanes are plant alkaloids that interfere with spindle fibres during mitosis. As already mentioned paclitaxel (taxol, pictured) is a chemotherapy agent derived from the Pacific yew tree (Taxus brevifolia). The drug is approved for use in treating many cancers including ovarian, breast and lung. Originally discovered in 1960s as part of a plant screening operation, the Pacific yew was virtually the only source of taxol until 1993 when alternative sources were sought for ecological reasons - in 1969 it took over a metric tonne of bark to produce 10g of paclitaxel. Now the drug is produced by a plant cell fermentation method.
Vinca alkaloids - In a different class of plant alkaloids from taxanes are the vinca alkaloids, with vincristine (pictured) being a typical example. These compounds are used as intravenous chemotherapeutics primarily in the treatment of lymphoma and, similar to taxanes, are mitotic inhibitors. Vincristine is derived from the leaves of the Madagascar periwinkle, Catharanthus roseus (also the source of the chemo drug vinblastine), and was approved as a cancer drug in 1963. However, the leaves of this plant had been used for ages as a folk remedy which is how the initial discovery was made and is a fine example of how 'alternative medicine', once tested, ceases to be alternative and becomes mainstream medicine. (This is not to say that all folk remedies have some underlying efficacy).
Topoisomerase Inhibitors - One method of killing rapidly dividing cancer cells is inhibiting topoisomerase. Topoisomerase I inhibitors include camptothecins (pictured) which are plant compounds derived from Camptotheca acuminata (Happy Tree), discovered in a systematic plant screen. Topoisomerase II inhibitors include etoposide, which is derived from the American Mayapple. Both are used as part of a chemotherapeutic strategy.
Anthracyclines - Anthracyclines are a class of drug that include epirubicin, daunorubicin and doxorubicin (pictured) which act as DNA damaging agents, inducing strand breaks by inhibiting topoisomerase II or causing oxygen free radical damage. They can also intercalate with DNA and prevents DNA and RNA synthesis. These drugs are commonly used in chemotherapy and find their origins in soil microbes. Daunorubicin and the related doxorubicin (and some related compounds) date back to to the 50s when they were isolated from the bacteria Streptomyces peucetius and shown to be effective against mouse tumours. Incidentally, the bacterial genus Streptomyces also produces a large number of clinically useful antibiotics (such as puromycin, chloramphenicol and streptomycin) and the anti-metastatic migrastatin.
Antitumour antibiotics - One of the antibiotics produced by Streptomyces is bleomycin (pictured) which gained FDA approval as a chemotherapeutic in 1973. This bacterially produced glycopeptide is used to treat testicular cancer and Hodgkin's lymphoma, among others, and works similarly to anthracyclines, generating oxidative damage and DNA strand breaks.
Of course, this is not a comprehensive list - there are other molecules found in nature that are used in cancer treatment. Some are based on natural compounds, but modified to be more effective. Others rely on modern synthesis rather than extraction from the source organism. One thing in common between the naturally derived drugs above and 'unnatural' modes of therapy is that all of them have been tested and shown to have some efficacy. Don't accept less from your treatment.