The traditional definitions of intercourse are (1) communication or exchange between countries, and (2) frequent or habitual intercommunication between people or things. But while these senses live on, the word now most often refers to sexual intercourse, even where the modifier sexual is absent. To use the word in its other senses, you have to make it obvious that you are talking about some other kind of intercourse, either by preceding the word with a modifier other than sexual (e.g., social intercourse, commercial intercourse) or by immediately making clear that the intercourse is between nonhuman things (e.g., intercourse between countries, intercourse between computers).
The phrase sexual intercourse developed in the 19th century as a polite or clinical way to refer to coitus between people. By the late 20th century, however, writers made the polite term even more polite by dropping the word sexual. Today, the doubly polite intercourse is used in reference to sexual intercourse much more often than is sexual intercourse itself.
Intercourse also has a rarely used verb sense—namely, to have intercourse with (intercourse here being of the nonsexual varieities). The verb has never been widely used to mean to have sexual intercourse with, though, so it does not have the same sexual associations as the noun.
In these examples, intercourse is used without the modifier sexual to refer to the sex act:
Couples matched by the church were instructed to refrain from having intercourse for 40 days. [Chicago Tribune]
Mr Cox has admitted having sex with the woman, but has denied rape, claiming the intercourse was consensual. [Telegraph]
A few times he pretended the president had suggested he and Romney have intercourse with themselves. [Slate]
The word is still sometimes used in its nonsexual senses, but examples such as these are not as easy to find:
I love the whoosh and squeal of a coffee machine and the sight of people relaxing and enjoying social intercourse. [Nelson Mail]
Communication is the livewire of modern social and economic intercourse. [AllAfrica]
The sacrosanctity of diplomats and their missions is among the oldest and most basic axioms of intercourse between civilized nations. [National Review Online]
Note how in each of these cases, the writer makes it immediately obvious that the intercourse is not sexual.