Taking a vitamin that contains beta-carotene could increase or decrease your risk of developing colon cancer. Which it might do, depends on you.
How can it increase your risk?
According to a study published in the Journal of the National Cancer Institute, smokers who took a beta-carotene supplement and consumed more than one alcoholic drink a day, doubled their risk of recurrent colon polyps.
How can it decrease your risk?
According to the same study, non-smokers and non-drinkers who supplemented their diet with beta-carotene decreased the occurrence of recurrent colon polyps by 40 percent.
So?
This study indicates that if you don't smoke and don't drink, taking a beta-carotene supplement (or multivitamin with beta-carotene in it) may reduce your risk of developing colon cancer. If you do smoke and drink, however, you may want to avoid supplementing your diet with beta-carotene.
Source: Baron, J. and Cole, B. "Neoplastic and Antineoplastic Effects of Beta-Carotene on Colorectal Adenoma Recurrence: Results of a Randomized Trial." Journal of the National Cancer Institute 95.10 (May 2003): 717-722. 28 Jun. 2006 [http://jncicancerspectrum.oxfordjournals.org/cgi/content/abstract/jnci;95/10/717].