There's certainly no connection to ovarian cancer...
Incomplete pregnancy and risk of ovarian cancer: results from two Australian case-control studies and systematic review.
Dick, Siskind et al, Cancer Causes & Control, November 2009, 9:1571-1585.
"Although full-term pregnancies reduce the risk of ovarian cancer, it has not been conclusively established whether incomplete pregnancies also influence risk. We investigated the relationship between a history of incomplete pregnancy and incident epithelial ovarian cancer among over 4,500 women who participated in two large Australian population-based case-control studies in 1990-1993 and 2002-2005. They provided responses to detailed questions about their reproductive histories and other personal factors. Summary odds ratios (OR) and confidence intervals (CI) derived for each study using the same covariates were aggregated. We found no significant associations between the number of incomplete pregnancies and ovarian cancer, for parous (OR = 0.98, 95% CI: 0.89, 1.08) or nulliparous (OR = 1.06, 95% CI: 0.75, 1.48) women, nor for the number of spontaneous or induced abortions and ovarian cancer for parous women (OR = 0.95, 95% CI 0.82, 1.09; OR = 1.08, 95% CI: 0.86, 1.36) or nulliparous women (OR = 1.2, 95% CI: 0.6, 2.4; OR = 0.8, 95% CI: 0.47, 1.38), respectively. A systematic review of 37 previous studies of the topic confirmed our findings that a history of incomplete pregnancy does not influence a woman's risk of epithelial ovarian cancer."
Mind you, I did find a recent paper that claimed that abortion was firmly linked to the risk of breast cancer, it was in a law digest and was written by Joel Brind, a genuine physiologist who hopes to "spare many women the agony of breast cancer", but tellingly also writes regularly for National Right to Life News.