I know that in Islam people who are not married to each other do not have the right to have sex, but what about married people? Are there any limitations on sexual acts that can be performed between a married couple?
Yes there are limitations in sexual intercourse in Islam. In fact Islam is very conservative about sex.
1. A man can approach his wife from any direction.
Your wives are a place of sowing of seed for you, so come to your place of cultivation however you wish and put forth [righteousness] for yourselves. And fear Allah and know that you will meet Him. And give good tidings to the believers. 2:223
This verse say you can approach your wife from any direction you want. At that time there were common believes that if you approach your wife from behind that resulted in children, the kids would have some kind of deformity. The Quran simply busted that myth.
2. Anal sex is strictly strictly forbidden
Although there is no direct verse related to it but there but this is general consensus among sunni Muslims that Anal sex between husband and wife is not allowed. It is also mentioned in tafsir of the above verse that sex must happen only where it is supposed to be, not in any other place.
Here are some hadiths that proves it is forbidden
Abu Hurairah, Book of Divination and Omens, Sunan Abu Dawood, 3895.
If anyone [resorts to a diviner and believes in what he says (according) to the version of Musa) or] has intercourse with his wife (according to the agreed version) when she is menstruating, or has intercourse with his wife through her anus, he has nothing to do with what has been sent down to Muhammad.
On the day of resurrection, Allah will not look at a man who had intercourse with his wife in her anus"—Narrated by Ibn Abi Shayba, 3/529; narrated and classed as sahih by Sunan al-Tirmidhi, 1165
and there are other available as well.
3. Sex during menstruation is forbidden
And they ask you about menstruation. Say, "It is harm, so keep away from wives during menstruation. And do not approach them until they are pure. And when they have purified themselves, then come to them from where Allah has ordained for you. Indeed, Allah loves those who are constantly repentant and loves those who purify themselves. Al Buqarah 2:222
This clearly states that sexual intercourse during the menstruation period is not allowed. Although a man can still fondle his wife in other ways, as the prophet used to do it. But his wife's private parts are not allowed for the husband.
4. Sex is not allowed during fasting
It is made lawful for you, in the nights of fast, to have sex with your women. They are a cover for you and you are a cover for them ... and do not have sexual intimacy with them while you are staying in mosques for I'tikaf. These are the limits set by Allah, so do not go near them. Thus Allah manifests His signs to the people that they may be God-fearing. 2:187
This says simply any type of sex is not allowed during fasting. This also means slight touching for satisfaction purposes is also not allowed as it may lead to more and can lead to disobeying Allah's command. Older people might have relaxed restriction as their desires are not that strong. This verse was revealed to allow sex during the nights in Ramadan. Because before that sex in the whole month of Ramadan was not allowed. But one sahabi made a mistake and that's when this verse was revealed to change the rule.
The following are debatable. More orthodox people tend to stay humble while other try to be more open.
The group that is humble
- You should not look at your women organs if there is no need even during sex
- There is no need for nudity unless the condition required. In case of intercourse, a woman may just allow his man organ and she may not need to expose the whole body. It is probably best to cover the bodies with a blanket to stay humble.
- A man should fulfill his wife's needs if his were met early.
More open group
The group that is more open would allow oral pleasures which group 1 does not allow. I personally think if you are not into it, never do it. If you are somewhat inclined and you think it will please your partner who demands it, you might break the rule. But at least keep it to yourself. Since there is no direct hadith related to it, it should be safe to do it. In sunni Islam a lot of things are imposed as precautionary. They are not forbidden but we don't do it just to be safe. So give yourself some room if you think you are that type of person.
Almighty knows best.