You don’t need to ask "what if", there are indeed chromosomal variations. So first, to supplement Lorileah’s post, is a little basic biology:
In humans, each cell normally contains 23 pairs of chromosomes, for a total of 46. Twenty-two of these pairs, called autosomes, look the same in both males and females. The 23rd pair, the sex chromosomes, differ between males who have one X and one Y, and females who have two Xs. So basically, males have 22+XY and females have 22+XX. This is usually denoted as 46,XY (male) and 46,XX (female).
There are many chromosomal mutations in non-sex chromosomes (genetic disorders), but you’re specifically asking about atypical sex chromosomes.
Here’s a list of sex chromosomes variations (the medical community refers to these as sex chromosome disorders). When the sex chromosomes result in ambiguous phenotypes (the physical traits of an individual), the people affected are referred to as 'intersex'. You can click on each link on the page below for specifics about each variation:
https://en.wikipedia.org/wiki/Sex_chromosome_disorders
This is a summary of the above for those of you who don't feel like clicking: the variations are 47,XXX, 48,XXXX, 49,XXXXY syndrome, 49,XXXX, 47,XXY Klinefelter syndrome, 45,X Turner syndrome, XX gonadal dysgenesis, XX male syndrome, XXYY syndrome, XXYY syndrome, XYY syndrome. Please note that these mutations are rare.
In addition to the above chromosomal mutations, there is Androgen Insensitivity Syndrome where a person who is genetically male (46,XY) is resistant to androgens. As a result, the person has some or all of the physical traits of a woman, but the genetic makeup of a man. This is rare as well, affecting 2-5 people in 100,000:
http://www.nytimes.com/health/guides.../overview.html
And here is an expanded list of intersex conditions from the now defunct Intersex Society of North America (ISNA):
http://www.isna.org/faq/conditions