I have never (even thought to have) tipped the maid.

I'm sorry if that is stingy, but I am paying high prices for the rooms I am using, and since maid service is included in the price, I don't need to tip.

It is not, in my mind, comparable to complimentary valet parking, which is not included in the price but is an added, optional perk.

If something is required then tipping is not usually necessary (for example, bellmen are doing something extra, so you tip them). An exception is waitstaff. If I am a big pig one stay, or I require extra assistance from the maids, then I may tip accordingly.