Affordable global service is a pipe dream for the time being.  There are a few global resellers which are cheaper than roaming but they still cost a fortune.  Your best bet would be an unlocked phone and pre-paid SIM cards from whatever countries you will visit.  A dual-SIM phone can be helpful as well.

Numbridge!

http://vimeo.com/60874365

Numbridge is the first international calling solution to offer the quality, affordability, and most importantly, the luxury of looking local -- while being global.
You’ll love it so much, you’ll want to call friends all over the world to tell them about us.

Either get multiple SIM cards or find Wifi and use Skype.

I have a wiko dual sim android phone. I have a Swisscom sim and a worldsim card also. So far using it a year and its pretty good, with auto charge for credit from my credit card so when n china etc never run out of cash. A bit more expensive than local sims but saves the hassle if you travel a lot I reckon.