It depends really.
If you want to be strict, it’s two. This is how the word has been used for most of its lifetime. It comes from the Old French cople (married couple, lovers), in turn from the Latin copula (tie, connection). We still use to couple as a verb in this sense, though it’s quite formal now.
Obviously if you’re using the noun a couple, with nothing after it, you’re referring to two people in a relationship. But what if you tell someone that you’ll see them in a couple of hours? This is where people get into arguments. Most of us probably agree that in this case, a couple of… refers to a low, but unspecified number. Like a few. Some people though, particularly those who take a prescriptive approach to language, argue that couple should only refer to a pair.
As usual, I think that we have to accept that the meaning has evolved over time, and a couple of… now means a few. But, I have some sympathy with the prescriptivists in this case. While teaching, I came to realise quite quickly that the way we use a couple of… is very confusing for a lot of English learners. A lot of people become aware that a couple consists of two people, and therefore assume that when we refer to a couple of somethings, we also mean two. This is compounded for Romance-language speakers, who are used to words similar or identical to couple which always refer to pairs, like the French couple.
So while I don’t think that we should always insist on using couple to refer to a pair, it’s worth considering how confusing the way we use the word can be for learners, and consider using a few when speaking with non-native speakers.