Ah, now we're getting somewhere... anthony, you left out the important bit about having remote sites all over the world!! That does, in fact, make a lot more sense.
jimbo sounds like he's already doing what you have in mind. To amplify a bit:
Two ways to approach this on first pass, from what I can see. If each location has a PBX or some similar CPE that can handle VOIP, then each can basically operate independently but have the system route calls over IP if they're going to HQ.
If they have an existing data-only WAN (i.e. T1s, leased lines, or whatever) then you're okay for the type of system you describe, but keep in mind that if you're talking routing voice over the public internet, you throw quality-of-service out the window and you're pretty much at the mercy of the health of the internet backbones around the world.
Finally, if you decide to pursue this, be aware that there are often unforeseen issues when dealing with phone service in foreign countries (specifically, those whose infrastructure is run by the government). I saw an article recently about a foreign government levying huge fines and threatening jail time when a company eliminated their "local" phone service and routed everything over VOIP. If I can dig it up I'll post a link...