[sinisterlee]

Was thinking the same thing. There are at least a dozen apps that you can get an SMS with like the one I mentioned TextMe. There's Google Voice.
Temp-Mail also has SMS services now.

It is quite country specific. There are the most services available for the US and the UK and less so for other countries.
Especially if the country requires SIM card registration.

But aren't all those apps in the Google Play store in most countries and if not can't you just spoof your location so the apps show up and spoof it so you can use the websites?
You can pick a phone number in the apps from dozens of countries.

Haven't checked all services but found some with partially working numbers (been rinsed for the most popular services).
Also got some weird sms's and calls from private numbers so probably best in most cases to go for a fresh number if you can get one anonymously.