I tip the same wherever I'm staying. Europe, South America, Asia, US, etc...
~$3 if I'm staying in a regular room and ~$5 if it's a suite and/or it has a separate tub/jaccuzi, shower, as I use both and create a little mess doing it.
I tip daily. The maids change daily, so it wouldn't be fair to the maid that cleaned my mess for few days and another maid scheduled to clean the room after the last night getting the entire amount. (I doubt very much s/he would cheerfully share the tip with the other maid).
Since I started tipping, I noticed that I do get "more" and "better" service after the first night. Sometimes it's nothing, but if I ask for extra "this or that", I get few "extras" instead of just one. Other times, the maids are proactive and start leaving more shampoos, more soaps, few more towels, etc.....
and I've also noticed that if I tip well, the word gets around and the overall service improves. The room service, the concierge, the bell boys, can't wait to help you with anything you may require, and that is true ALL over the world......