According to the killer (or kamikaze) sperm theory, men produce specialized sperm that will seek out and destroy competitor's sperm. So, if a woman has had sex with more than one men, killer sperm from each suitor will try to take out as many of his competitors' viable sperm, thus increasing the odds of him being the one who gets her pregnant.
Now, research has addressed this hypothesis:
No evidence for killer sperm or other selective interactions between human spermatozoa in ejaculates of different males in vitro Moore, H.D.M., Martin, M. and Birkhead, T.R. (1999)
This study examines one of the possible mechanisms of sperm competition, i.e. the kamikaze sperm hypothesis. This hypothesis states that sperm from different males interact to incapacitate each other in a variety of ways. We used ejaculates from human donors to compare mixes of semen in vitro from the same or different males. We measured the following parameters: (i) the degree of sperm aggregation, velocity and proportion of morphologically normal sperm after 1 and 3 h incubation in undiluted semen samples, (ii) the proportion of viable sperm plus the same parameters as in (i) in 'swim-up' sperm suspensions after 1 and 3 h incubation, (iii) the degree of self and non-self sperm aggregation using fluorescent dyes to distinguish the sperm of different males, and (iv) the extent of sperm capacitation and acrosome-reacted sperm in mixtures of sperm from the same and different males. We observed very few significant changes in sperm aggregation or performance in mixtures of sperm from different males compared with mixtures from the same male and none that were consistent with previously reported findings. The incapacitation of rival sperm therefore seems an unlikely mechanism of sperm competition in humans.
Download the paper here.