The one truly global handset is Iridium. The 9555 & 9575 are stand alone units while the Iridium GO! pairs via blue tooth with your cellular phone.
These options fall under Iridium's global network of 66 low earth orbiting satellite that spend about 11 minutes overhead and then hand off to the next satellite providing coverage in your area.
The Inmarsat handset the ISAT2 is a popular handset that while fantastic for a large portion of the planet fails around the Arctic and Antarctic circles. It is also easier to lose connectivity due to requiring line of sight to a satellite over the equator.