In the beginning of a dating relationship, I assume that the guy I am dating is on his very best behavior, that he is putting his best foot forward and trying to make the best first impression possible. When a guy pays for a date, it shows me that he is trying to be courteous, respectful, and generous, that he has somewhat traditional values regarding dating, and that he had at least some interest in making a good impression.
That being said, I have no problem with free or low-cost dates. When I go out on a date with someone, I am trying to decide if I enjoy that person's company and if I feel a connection towards them, if we have things in common, etc. Some of the best dates I have ever had were simply hanging out with someone, talking, playing video games, walking around a park, or watching a movie on TV. I don't expect a man to break the bank trying to impress me, and I understand that especially in these tough economic times that he may not have a lot of money to spare for dating. Also, I certainly wouldn't want a man to extend himself beyond his means just to impress me.
However, when a guy asks me out to dinner or a movie, I expect that he should be willing to pay if he was the one who extended the invitation. If he doesn't have the money to go out to dinner, that's fine... ask me to do something else that either costs less or is free. It makes no difference to me how much money a guy spends on a date, but I think it is in poor taste to invite a girl on a date if you have no intention of picking up the tab. Going back to the whole "first impression" thing, I assume that the first date is someone's very best behavior- if "going dutch" or paying the whole tab is his best behavior, what will things be like a few months down the road?
Once a relationship has been established, I have no issue with splitting the bill more often or even paying for some dates. At that point, I think it becomes more about communication, partnership, and "give and take" so that the relationship does not become one-sided.