I first try to see why the opponent would offer a draw, I ask them by chat usually. If it is because they have to go, then I accept, if that is not the case then I decline.
Not Accepting Draws

I could care less if you have to go. Manage your time. If you have 10 minutes, play a 5 minute game, don't play a 15 minute game. If you have 5 minutes, play a 2 minute game, not a 4 minute game. Pretty simple.
I accept a draw when I feel I am worse or it is a dead draw. If I feel like it's equal but complicated, or that I'm better, forget it - DECLINE!

I have definitely been on the position were I have to go and the opponent does not accept the draw, even when he/she has a losing position

@eaguiraud, I agree--I try to the same thing and have the same experience. I usually play 5 minutes, but sometimes I'll get a call from work that I have to take and I know will take longer. In that case I offer a draw, but usually end up resigning.

When a player offers a draw, I usually either already know I'm about to win or take a closer look at the board because it's likely they saw something I didn't. Very rarely have I seen anyone offer a draw that didn't mean I was winning, and they were trying to salvage what they could of the situation. (My rating is still low though.)
I've been playing a few games, and suddenly have had to leave--the game is in no clear victory for one side at the other, so I offer a draw. The opponent hardly ever accepts it? What is the etiquette on draws and offering them? I always try to accept, because I don't know the circumstances of the other player.
Thoughts?