Two is sufficiently complicated.

Life obviously considers two is a good trade off between genetic diversity and the 'cost' in energy expenditure in creating different genetic types for reproduction to get started. More 'sexes' could be classed as too expensive to sustain sometime in our distant ansestory.

If there were three sexes instead of two, the chances of successful reproduction would be reduced.Getting three entities together at the same time is going to be more complicated than getting two together at the same time.Also, consider a system where there is only one breeding group within an area. With a species with two sexes, one of the two has to die for reproduction to be impossible, whereas with a three-sexed species, if one third died reproduction would be impossible, so it is more likely that this species would fail to reproduce, putting them at an evolutionary disadvantage.

In a species where fertilisation occurs within one organism, instead of all over the place - as happens with most fish and many plants for example - one organism has to physically reach the other some how. It gets harder for enough organisms of the right genders to be in the right places at the right times the more genders there are. Barnacles, for example, don't move very much at all, which is why compared to their body length, their penises are gargantuin. When a barnacle is fertile, it is fertilised by any male barnacles in the area (usually more than one tries - it gets messy). If two non-female barnacles needed to be near a female, or in some sort of line, the chances of an apropriate barnacle 'constellation' would be greatly reduced. Another factor is population stability; In humans, if everyone has two children before dying, and each of their children has two children etc. then the population remains stable. And the same applies to any two gendered species. If their where three genders we would all need to have three children. So for an 'n' gendered species, 'n' organisms would need to meet eachother, (not necessarily all at once) resulting in children, and each would need to repeat the process at least 'n' times, just to avoid extinction. When 'n' is large they simply won't have the time or the means to do so (I am assuming they don't just let it waft on the breeze). As to why their aren't less than 2 human genders, I will have to leave it to Ian Stewart and Jack Cohen to explain, by suggesting that you read 'Evolving the alien'.

The answers above all assume that all three genders must meet to conceive.What if A could mate with either B or C etc, rather than requiring the presence of all three? Would this not increase, rather than decrease, the opportunities for copulation?Perhaps the two-sided structure of the DNA helix provides another part of the answer. Each parent supplies one of the two strands of DNA to the child; a two-gendered species is probably the simplest way of doing so.