90 days or 180 days, US Passport (no visa)

For the UK it's generally 180 days from the most recent entry date for a general visitor unless there's a suspicious pattern that makes somebody think you're trying to contravene the immigration laws.

For Schengen Europe it's 90 within the last 180.

You'll have to do your own finger counting based on the above.

On a US passport, you can stay 6 months, or closer to the 180 days. The UK is less clear whether that is 6 months from your first entry, when it resets, whether the two weeks out extended it, etc. But for your purposes, it looks like the six months works.

As for staying longer, you could go back to mainland Europe and the Schengen zone, there you get 90 days in a 180 day period (maybe that is where you are getting the mix-up) you spent 14 days or so of that so far, so you still have a couple of months plus.

If you want to extend beyond that, I would find someone in UK immigration to verify if after a couple months in the Schengen zone on return you would be granted entry.

Using the OP's phraseology, I continued with 180 days while Home Office guidance uses the phrase six months -- and that's very generalized.

The Brits have a lick of sense. They've put out guidelines and left the decision up to the Border Agency / Border Force officers. There is no magic formula, or exact number of days, or specific time away requirement. As long as you're not sneaking around trying to be a resident, you'll have no problem. Make them suspicious and it ends right there -- maybe at zero days -- probably without much chance of appeal. The guys and gals sitting on those desks are not the village idiots.

Back in 2011 there was a "fly on the wall" TV series about the UK border force and how they operate. The first in the series is here: http://www.youtube.com/watch?v=dMgfuM0Ylcs
Some of the people trying to talk their way in at Heathrow are so obvious it is hilarious.

Do you have an entry stamp (entry into the UK) in your passport? Last time I looked (a very long time ago indeed) it used to state the date entry had been granted until.

As Nigel has said you have to look at your passport to be sure. The officer may have granted you a fresh six months or may be less although if that had been the case you would probably have been told. Going out of the CTA and back in again may start to raise suspicion that you are trying to prolong a stay in the UK over six months duration in total.

It sez 'Leave to Enter for Six Months' and the date is the date in -- judging by the other day which is about as far back as I can remember.

Mine has lots of overlaps in dates and it's a blobbed mess, but it looks like there's a fresh stamp each time.

Thank you for all your lovely responses. This has been very helpful!

I have a stamp on my passport on July 18th that says "Leave to enter for 6 months" and then received the same stamp on September 2nd, when I returned from Germany. Does this mean my clock restarted on the 2nd of September, or is July 18th still the marker?

Also, I am going to the Netherlands for a few days in October - will I need to worry about or be careful about what I say when coming back into London? Would it be safer to stay in the UK during this stay, or is it better that I am traveling? While it doesn't seem like l am doing anything wrong or illegal by staying in the UK for 6 months, they always grill me at the airport why I am staying so long, and I get nervous, afraid of saying the wrong thing.

You will have 6 months from your second entry point.

Providing you aren't pushing towards that when you take a trip out and back you should be fine. It isn't a strict legal limit, but as a rule of thumb you start to raise flags if you are going to be in the UK for more than 6 months in any 12.

Marco's statement is accurate.

The Netherlands trip will get you a new British stamp when you return which will govern. Time in the Netherlans will count toward your Schengen limit.

As for what to say, you answer all questions completely and truthfully. It's pretty simple.

I wouldn't worry about heading to the Netherlands for a few days. And yes, it seems the UK "grills" you a bit more than other countries, just be honest and tell them why you are there. They may be suspicious that you are working in the UK...which would give you reason for worry if you were. I am sure they hear all sorts of stories and I usually see several individuals sitting off to the side waiting for further questions when I enter.