It varies. I can look my wife in the eye with no difficulties at all, although I do realise that my timing and duration compared to "normal" is probably off, but it doesn't feel awkward or wrong in any way. To a degree, it's easier with familiarity, progressing from feeling a bit off and not knowing when is appropriate, to it feeling uncomfortable (raised heart rate, generally low level anxious response) through to with strangers, superiors or people I don't particularly like where I actually feel pain, like a sort of stabbing headache in a specific point in my brain if I maintain eye contact (yeah, that makes job interviews great fun).
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"You're never more alone than when you're alone in a crowd"
-Captain Sheridan, Babylon 5
Music of the Moment: Radiohead - In Rainbows