I'm off to the US in January and had an email reminder about needing a visa waiver thing to enter the country. The links on the email are for the Office of Homeland Security and asking for a charge of £16 to get the visa waiver - I've been to the US a few times before ( not recently mind ) and don't ever remember having to pay for a visa to enter the country, so is that correct??

They introduced a new requirement some time ago that you had to fill in some sort of application for entry over and above what used to be the case of just getting a visa. In other words without the ESTA you won't get in even if you have a valid visa.

I think once you have one of these ESTA's they last for two years.

You see, this is one of the reasons I'm going to let my passport expire next year.

So you don't fill in that little green card thing on the plane anymore then?

They introduced a $14 charge a couple of years ago - I got one just before the charge came in. The official link is https://esta.cbp.dhs.gov/esta/. Watch out for a lot of other sites that will charge somewhat more than that to apply on your behalf. This replaces the 'green card' that you used to fill in on the plane and it is required before you travel. You won't be allowed to check in for the flight without it.

They introduced a $14 charge a couple of years ago - I got one just before the charge came in. The official link is https://esta.cbp.dhs.gov/esta/. Watch out for a lot of other sites that will charge somewhat more than that to apply on your behalf. This replaces the 'green card' that you used to fill in on the plane and it is required before you travel. You won't be allowed to check in for the flight without it.

Some years back, we flew in via San Francisco, filled-in the two-part card and handed them the "Entry" part.
The idea being that, when you left, you should hand them the "Exit" part.

After a few days in SF, we flew domestic to LA to get the flight to Auckland.
At LA airport we didn't go through any barrier between domestic and international and boarded the Auckland flight.
We merely showed our boarding cards (issued at SF) at the boarding gate.

When I got home several flights later, I was still in possession of the the "Exit" card.
The US might therefore think that I am still illegally in their country.

I do hope it's all a bit more secure by now.

Nonetheless, unless they've repealed the Patriot Act, they can chuck visitors in jail for months without trial if they imagine that they might be terrorists or a bit shifty.
That could be a bit inconvenient so, being that I haven't officially left the US, I don't want to confuse them by going in again, so I shan't be risking it.
Ever.

I had an indefinite visa, so had to carry my old passport around with me when visiting the US. I also had to complete a different colored card on the plane - same questions, just a different coloured card. At the bit that asks "do you intend to enter the US to cause civil unrest or insurrection?", I always answered "sole purpose of visit". Never got pulled once.

On your last point, I'm not only in total agreement, I seriously doubt I'll ever board a plane again, to fly anybloodywhere

FFS!!!!
It really is simple.
To get into the USA you either get an ESTA for $14 which will take about 5 minutes to process on the inter web or you can apply for a visa at the US embassy and hope they can process it with their current troubles.
Your choice.

Somewhere in a box in the loft exists an old British passport of mine from 1973 with a US visa with "Indefinite" stamped on it, if I had money to burn I could be tempted to spend eight hours on a plane just to test it.

Yeah, I know.
Just a bit of harmless thread drift ...