Earlier quoted context omitted.
Some online banks (don't know how widespread this is) allow you to create "virtual card" that expire either after 1 purchase or at a specific date (and with a set maximum of budget). I use them for every single purchase I make online, it's inconvenient but at least i've never entered my real card info anywhere.
That sounds like a lot of work. At least in the US you are not responsible for fraud. (I think the law may have like a $50 liability thing, but Visa/MC waive). So it's better to just not do this, and every 3-4 years when my CC is stolen, call them up - dispute the charges, get a new number. Takes For what it's worth, the 2 times my number got stolen in the last 6 years, one was from a rogue agent at a hotel in Chicag…
You can even scan the card via webcam or copy the details to clipboard.
The virtual card also limits itself either to single transaction or single store so it can't be used even if compromised on store level.
It's pretty simple process (<30sec) and it's really useful.