I understand there are many options and models and different coverages of the world.
The one I will be using later this year will be an Iridium phone, their worldwide coverage does appear to be the best of those available. Lots of phones available on e-bay but do your own research as to where you want to go. also be aware of the call/data costs which are much higher than what you normally experience.
In addition to Pat’s question, does anyone know of free software for connecting a satellite phone to a laptop.