During regular sexual intercourse between completely healthy people, the blood cells should not mix. However, if either partner has abrasions or sores in their genital area, they may have an open conduit to their blood stream. Such openings can be microscopic, so the may not be visible or able to be felt. Many sexual transmitted diseases are present in the vaginal secretions and semen, so the infections can be transferred from the infected person, directly into the bloodstream of their partner, via these tiny openings. Condoms can greatly reduce the risk of blood cells or genital fluids mixing, but abstinence is the only way to insure this completely.

The answer to your question depends on a couple of things.

Semen is composed of sperm (male reproductive cells) and seminal fluid (sugar and liquid that transport the sperm).

Vaginal fluid is primarily fluid discharged from the cervix.

During sex these fluids are exchanged and do not usually contain blood cells. However they can contain other things that are also found in the blood stream.

Viruses present in the blood stream can also be found in semen and vaginal fluid. The one you've probably heard most about is the HIV virus which causes AIDS.

Other viruses in the blood stream can also be transmitted from one person to another via semen or vaginal fluid.Blood cells do not have to be present in order for the virus to be transmitted.

There are some circumstances which make it likely that blood cells can also be exchanged during sex. If one person has a sexually transmitted infection (which might result in an off-odor or off-color discharge) then the increased irritation during sex can easily lead to bleeding.

Increased inflammation at the site of the infection also brings more blood cells to the surface.

Another circumstance in which blood cells are exchanged is during rough sex that leads to tears in the skin or vaginal wall. Using a condom will prevent (98% of the time) any cells from being exchanged during sex except skin cells in the area that the condom does not cover.

Blood cells won't usually mix during sex. But you never know if there are little wounds, and then a few blood cells could go in or out through the wounds or weak spots in the skin. Women will be losing blood cells during their periods, of course, so some of them could get into the guy if there was a weak spot in the skin. You never know for sure what all is going on 'down there', so you want to be careful in case there is a problem. You could probably learn more by investigating the safety precautions for AIDS. That's a similar question - is something going to go from one person's blood to the other person's blood during sex?

Generally, no, although it is possible. There is a lot of variation in what bodily fluids are exchanged during sex, depending on what organism we're talking about and what kind of sex that organism is having.

In humans, blood is usually not one of those fluids. Sometimes during human sex, though, skin or other tissues can be abraded or cut unintentionally, and there might be some small amount of bleeding. The amount of bleeding might be too small to notice, but it may still be there. If that happens to both of the people involved, then, theoretically, blood (and therefore blood cells) could mix.