I've only had it happen for over-the-phone purchases, and when using a debit card to transfer about £5000 via TransferWise.
I haven't been to the USA for a while, and most other countries have a working (not new) Chip+PIN system, but I assume magstripe transactions would be considered higher risk too.
It's been easy for me - I call my bank ahead of time and tell them where I'll be going,the duration of my stay and my number while I'm there. They usually ask for a backup number just in case I'm not reachable.
