Regarding marriage in Islam, it is not mandatory for anyone (male or female) to marry.
Allah (God), in the Quran, recommends marriage but does not state that it is a fardh (compulsory) act. However, as the Prophet Muhammad engaged in marriage, the act of marriage is considered a sunnah (tradition of the Prophet).
As Allah says in the Quran's thirtieth chapter, titled Ar-Rum (Rome), verse 21:
Among His signs is that He created for you spouses of your own kind in order that you may repose to them in tranquility and He instilled in your hearts love and affection for one another; verily, in these are signs for those who reflect (on the nature of the reality).
One notices immediately that the purpose of finding a spouse is, first and foremost, for both parties to find tranquility in each other. In this case, that comes with emotional as well as spiritual tranquility. However, the physical aspect of marriage and the fulfillment of physical desires is also of importance, as this is considered part of human nature.
Also, it is interesting to note that Allah says that He has created for "you" spouses of "your" own kind—this does not signify gender, and it illustrates that this is the recommendation for both men and women.
It is written that the Prophet Muhammad once said, speaking about marriage,
It spares one looking at what one should not, or lapsing in adultery. (Reported by At-Tabarani and Al-Hakim)
Now, regarding both society and the individual, a married person has a responsibility to his or her own husband or wife, as well as a responsibility to society in that adultery can become something that is damaging to the community as well as the individual.
There are those whom Muslims are explicitly not allowed to marry. According to the Quran, this includes the following:
And do not marry those [women] whom your fathers married, except what has already occurred. Indeed, it was an immorality and hateful [to Allah] and was evil as a way. Prohibited to you [for marriage] are your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters, your brother’s daughters, your sister’s daughters, your [milk] mothers who nursed you, your sisters through nursing, your wives’ mothers, and your step daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you. And [also prohibited are] the wives of your sons who are from your [own] loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful. And [also prohibited to you are all] married women except those your right hands possess [i.e., slaves or war-captives who had polytheistic husbands]. [This is] the decree of Allah upon you. And lawful to you are [all others] beyond these, [provided] that you seek them [in marriage] with [gifts from] your property, desiring chastity, not unlawful sexual intercourse. (Quran, chapter 2, verses 22–24)
Additionally, a Muslim man is allowed to marry another Muslim woman, as well as a woman who is Christian or Jewish (Ahl al Kitab, or People of the Book). For the most part, a Muslim woman is not allowed to marry a Christian or Jewish man and must marry a Muslim man, since children from a marriage usually fall into the father's custody, and this endangers the chance of the children remaining Muslim, in case of a divorce. However, the ruling on this varies depending on context.
Therefore, it is not a state, or states, that stipulates whom a Muslim is allowed to marry. Rather, this is decided according to (but not limited to) the context, meaning that the nature of the individual, the era, the state of affairs surrounding the marriage, specific belief systems, and so on would all be taken into account if one were to ask the advice of a knowledgeable, just, and reputable scholar of Islam their opinion of a possible marriage.
That being said, if a Muslim individual were to disregard the advice of such a scholar or, more importantly, the teachings of the Prophet Muhammad, the consequences could be seen as lying between the believer and Allah.