Not having time to do a thorough survey, we find a number of interesting word choices of which three are relevant. When Avraham agrees to Sarah's proposal to have sex with Hagar to produce an heri, the word used is "Vayavoh," and "he came" (no bad jokes please, too obvious). When Schem, the son of Chamor, rapes Dinah, the word is "Vayishcav" (which is joined with "Va-ya'aneha," and he humbled her).
Not to make a grand point, but it appears to me that "to know" is not merely to have sex, or even to have sex that produces a child (as in the case of Avraham and Hagar). It seems to me that "Vayaidah" suggests, at the least, a level of intimacy as well as a physical act.
From this we may take an important lesson for our own sexuality. there are many ways in which we can approach our sexual partners. At the worst, it can be violent and described in a purely physical way. Vayishcav describes a physical action. Chamor treats Dinah with the same lack of concern that a man might have toward any place where he lies. Even if not physical, it can lack true intimacy and emotional connection. Thus, Avraham merely comes to Hagar (Vayavoh). While we have no evidence that Avraham forced himself on Hagar unwillingly (he merely comes to her, he does not force her), there is no intimacy ever shown between. Them. When Hagar acts haughtily to Sarah and Sarah asks Avraham to intervene, Avraham replies "your handmaiden is in your hands." To Avraham, Hagar is merely a servant and his sex with her is merely to satisfy the clan need for an heir. Even later, when Sarah demands that Avraham send away Hagar and Ishmael to protect Yitzchak, the text informs us that Avraham hesitates because he loves Yishmael. Hagar does not enter into the equation.
Now we may see the importance of the word "Vayaidah," "to know," to describe not merely sex but intimacy. Adam and Chavah are, as God commands, to "cleave to each other" and "become one flesh." This should be our model, as "therefore does a man leave his father's house" and marry, beginning his own household. In our own sexual relations with our own partners, therefdore, we should aspire not merely to physical satisfaction (vayishcav) or even a willing exchange of pleasure with a willing partner (vayavoh), but should rather seek the level of true intimacy that marked that magical moment when Adam and Chavah came to truely know one another.