Short answer.

In Europe and US, for someone carrying US passports, sometimes they stamp, sometimes they don't. There's really no particular pattern.

But if you ask, then that'd definitely raise a red flag. Either way, especially if you say you don't want it stamped. Expect much closer scutiny and many questions if you ask.

Tiff:

"are you saying that it is every person's right to not allow (sic) their passport to be stamped?"

Of course not. What have I said that sounds remotely like that?

What I said is that it's ridiculous (and in my view the sign of unhealthy subservience to authority) for posters to tell you you shouldn't ask. If you're coming here legitimately it's impossible - unless you're paranoid, or from a country with no concept of the rule of law - to imagine there might be adverse consequences to such a request.

The official has the right to decide whether to honour your request. He absolutely does not have the right (nor is it possible to see why he'd have the inclination) to treat you in any way differently because you made it.

Assuming officials are accountable grown-ups is essential to ensuring they stay that way.

"In my experience, the only time your passport gets stamped is if you ask."

This is not my experience with UK (Heathrow) - have been there approx dozen times in the last two years and have approx a dozen UK stamps in passport

Your passport will be stamped entering the UK - i have zero doubt about that regardless of your pleas. You could even be asked to show money or evidence of funds - credit cards, etc. though this is mainly for backpacking types. UK has been traditionally fearful of folks who plan not to tour but to stay and tap into the generous dole. Thus passports are inevitably stamped with the date of entry and the words "leave given to enter the UK and stay not longer than xxx months" Good luck asking not to have the passport stamped!