One date. I can see keeping an open mind and going on a single date with someone, but that is the limit. Going on dates with people you normally wouldn't consider is good as it opens you up to new experiences, but if you don't feel a spark by the end of the first date then just move on. You will just be leading him on as he develops feelings. Women trying to give guys a chance beyond that, just make the guys feel used and lead on.
I would honestly say you shouldn't go out with someone at all if you don't find them physically attractive. If you're thinking attraction will develop though and it hasn't happened after a few dates, I would say to move on. It's not fair to the other person. Everyone deserves to be with someone who finds them attractive.
So, if the attraction isn't there, then let him down gently and move on so you can find someone you are attracted to and he can find someone who genuinely likes and is attracted to him in return. Leading people on isn't cool (I'm not saying you're intentionally doing that, but the longer you stay with him knowing that you don't feel the same way, the worse it will be for him).
I won't date a guy unless we have been friends first. I want to get to know their personality and don't want the pressure of romantic feelings to be the driving force in me dating them. If you're not physically attracted to them, I wouldn't date them. If you see potential, then try it out for a month or two. See if things change. If they don't, then cut your losses.
As long as you can stand it. You don't owe him your affection for being nice. You've got a single life to live, spend it in the company of people you find wholly attractive and don't feel bad. Attraction can develop over time but it's not like a switch you just flip on.
I went on a couple of dates with a guy recently and whether physically / as a person, I just didn't feel that excitement that I felt I should with something new like that... so I cancelled the third date... I felt like a bitch but I thought it would be worse to keep seeing someone and giving them the wrong idea then to just back out at a later date.