I receive this question from readers fairly often, but I don't usually have much of an answer, or for that matter much experience (when I roomed with Daniel Klein, he and I split the rent evenly). Now there is an interesting study. There are 42 datapoints and definitely some selection bias, but it's better than anything else I've seen. It examines for instance whether people first pick rooms and then set the prices, or first set the prices and then pick the rooms, or draw from a hat. It measures which factors most affect the rent splitting, with "No door" and "Private shower" coming in first and second respectively. The factor of importance for an apartment with the biggest standard deviation is size of the common area. In the survey, personal space is what people are willing to pay the most extra for. Opinions about the importance of windows have a high variance.
Here is their rent calculator, based on the above study.