As a brit with visa-free entry to the USA, I wondered if I could go to the USA,

then border-hop to Mexico returning to N. America on a border stamp ?

 

And I also wondered (apart from SE Asia);

where in the world can "Visa on Arrival / Border-Hopping" be done continuously?

 

 

No, the US isn't going to let you do that. The Visa Waiver Program lets you enter the US for 90 days, and a quick border hop doesn't reset that and get you another 90 days. My understanding is that there's no hard and fast rule about when the 90 day resets and it's up to the immigration officer to look at your history and decide if you're trying to stay in the US for too long. (Which I guess is the same thing Thai immigration officers do; it's not like you can stay in Thailand continuously using visa exempt entries either).

 

However, the rumored rule of thumb is that it resets when you've been out of the US longer than you've been in the US. So if you've stayed in the US for the full 90 days, you'll need to leave for 91 days before you can come back and get another 90 days.

UK passport holders can apply for and receive a 10 year multi tourist visa if they can show reason for staying 6 months at a time. 6 in then 6 out.