Does physical desire for someone else, without any action count? Hardly. It'd be stupid for me to be upset at Lady Drak for lusting over Brad Pitt, just like it'd be dumb of her to be mad at me for having naughty thoughts about Milla Jovovich.
What about a strong emotional connection with someone without any physical contact?
This is somewhat situational. There's a lot of variables to consider.
What about physical intimacy, but without any feelings?
Providing you gave yourself willingly ["You got raped! You don't care for me! I'm leaving you!" doesn't apply], I'd say yes, even drunkenly. The only exception with the drunkenly thing is if you don't remember. I say that because I have a friend who got drunk and woke up next to someone, and she told him they screwed, and everyone else at the party was like, "Dude, **** no. You yakked in the ****ter, and passed out with your pants off. We just tossed you in that room beside her passed out ass."
What about a one night stand?
No, that's just cheating.
How about phone or Internet sex?
Internet sex, hell no. By that logic, everytime you *********ed to porn that has the same "star" would constitute as cheating. Does phone sex even EXIST anymore? Even so, I'd say no, especially if you call one of those sex lines, because, well, they're men.
What about distance (the different time zone thing)? Are affairs limited to only those who are married or do they apply everyone?
I'd say that if travel time was more than a few hours, it wouldn't apply. Of course, an exception would be if I were to drive back to Virginia like once a month to be with my high school crush. In terms of semantics, I'd say yes. Cheating is universal, but an affair is exclusive [married/engaged].
For that matter, how would you define "affair?"
A continuing emotional or physicial relationship with a person/persons outside of your commited relationship.