Emails circulating since 1999 have stated that antiperspirant use is a cause of breast cancer. Urbanlengends.com listes this as unsubstantiated and Snopes.com listed it as 'undetermined'. One of the main proponents of this 'hypothesis' is Kris McGrath, MD from Northwestern University Medical School. His article http://www.ncbi.nlm.nih.gov/pubmed/14639125 suggested that early use of antiperspirants and frequent axillary shaving were more common in women diagnosed earlier in life compared to use adn frequency in women diagnosed when they were older. Circumstantial and circuitous logic that has never been substantiated. The myth has been rejected by essentially all prominent breast cancer specialists and organizations including the American Cancer Society which has a nice layman's discussion of the issues http://www.cancer.org/Cancer/CancerCauses/OtherCarcinogens/AtHome/antiperspirants-and-breast-cancer-risk
So don't worry - you can shave your underarms and use antiperspirant without raising your breast cancer risk!!
