I think it varies a lot depending where you live, who is doing it, and if they bring their own cleaning supplies. I would say $20—$25 an hour is fairly typical per person if you supply everything. If it is a professional cleaning service it would be more like $40 per person and they bring everything with them. If it is a neighbor, like a teenager wanting some extra money, then more like $15—$20 and it won’t be as thorough usually, but satisfactory.
Some people don’t price by the hour if you are going to use them regularly, they give you a price per visit. Three bedroom around $2,000 sq. ft. will be around $125—$150 assuming it is all a surface clean, not including window or inside of a refrigerator, although most housekeepers do clean inside of the microwave. Some include changing the bed linens and some don’t. You might get it for $100 if it is weekly and overall you keep the place clean.
Edit: The cleaning services like Merry Maids are usually great if you need a really good very thorough clean. They are more expensive, but they send in 2 or 3 people at once, and they clean top to bottom in half the time.