I don’t have much in the way of social grace, but I enjoy the occasional dance. Something I never quite understood is what you’re supposed to look at when dancing somebody. It feels extremely awkward to maintain eye contact, but looking away seems rude too. It’s that much more difficult when the partner is attractive. So, what’s etiquette and non-creepy?
Edit: If it matters, I’m a guy.
By “partner dancing,” you mean waltzes, polkas, hambos, things like that?
I always tried to look into my partner’s eyes and smile like, you know, I was having fun and enjoyed her company. Hopefully she wouldn’t have been dancing with me out of pity or some other obligation, so she would do the same to indicate she enjoyed my company.
Occasionally, you have to glance away to see where you’re going, but as a rule, I’d say keep your eyes on your partner’s face and smile.
Of course, if you’re talking about more freestyle dancing, I don’t think it matters where you’re looking, so long as you don’t move too far away from your partner. If you’re really good, you can improvise steps like Vincent and Mia in Pulp Fiction.
Ballroom dancing, eyes on your partner, until it’s time to turn, then look where you’re going, then resume gazing fondly into the eyes of your partner. It’s kind of the whole point.
Agreed–everything I’ve heard says that ideally you’re looking into your partner’s eyes, although if you can’t stand that you look vaguely over your partner’s shoulder (and if your partner is looking over your shoulder, you can do the same). Partner dancing is kind of formalized flirting, and someone that’s agreed to dance with you is unlike to object to smiling eye-contact with a flirtatious feel.
It matters. Guys lead; you should be looking down the line of dance and around you, so as to guide you and your partner around the floor. In the dance world, the technical term for this is “floorcraft”.
A related matter is “frame” – your posture and hold. It varies from dance to dance, but no, the gazing-into-the-eyes business isn’t part of the USA Dance standards (official organization; covers competitive and social dancing):
The lady should be looking a bit vaguely into the distance, also keeping an eye on traffic.
Hmm. I’ve always thought that if she isn’t looking at you, she’s bored. 
I guess it depends on who your partner is (somebody close or a casual acquaintance).
Don’t blink. Don’t even blink. Blink and you’re dead. Don’t turn your back. Don’t look away. And don’t blink.
Well, if you’re taller than she is and she’s wearing a low-cut dress…
I was wondering how long before somebody said the real answer!
whatever protrudes or jiggles is what you should watch.
Like Ham Jordan, you don’t need to go to Egypt to see the Pyramids. 
You should look at your partner once in a while, but staring constantly into each other’s eyes sounds sort of sappy. If you’re that besotted, get a room. Otherwise, pay attention to what you’re doing, navigate the floor so that you don’t barrel into other dancers/couples.
When I was ballroom dancing, the standard was always to look to your left, over your partner’s right shoulder. This was the “default” position. Looking in each other’s eyes was fine once in a while, like when you were talking, but to constantly stare into your partner’s eyes was considered creepy (unless you were already in a romantic relationship with them).
Additionally, once you were beyond beginner or low intermediate, you were ALWAYS doing something other than moving in a straight line. For this, the man would mostly have his head on a swivel, making sure that the floor was clear for the current or anticipated next step / pattern. The man’s first job was always to protect his partner and that meant very good situational awareness. If there was any danger of running into (or stepping on) another couple the man was supposed to prevent that, even if it took abruptly stopping, extending an arm to fend off another couple, etc.
Now, talking while dancing complicated steps was a whole 'nother thing. It definitely took very good multi-tasking skills. (I’m referring to dancing creatively, not a choreographed routine.)
J.