Skype with a bit of credit is an excellent approach- you can call any number in most countries and I believe that 800 numbers in the US generally work (that becomes important when you only have an 800 number- it won't save you money). A half hour call from China to Canada, for example, is something like a dollar. Some countries rip you off with extra fees (eg for mobile phones) but these are just the countries that will make it illegal to use VOIP, and may block it. Some countries block Skype too, but you can often get around that with a VPN.
Aside from emergencies, some folks are just more comfortable using a real telephone- they don't have to know what is going on at your end, so the credit can serve both purposes.
If you install the app on your phone and computer you can make calls wherever there is reasonable (often free) Internet. I was in the arrivals lounge of an Asian airport last fall and a man was at the pay phone going ballistic because it was costing him $50 or $100 US in long distance fees to work on clearing up some kind of a travel snafu. I have cleared up a number of such problems with little extra stress and almost no unnecessary cost using a combination of IM, Skype out, email and (when justified) a local SIM card.
I do have VOIP phones and could, in theory, use those directly, but my experience in getting them to work reasonably well requires using a SIP server that is near to your current location. So I would have to have a list of sites and change the settings on my VOIP software (I have Voiper). The rates are cheaper(maybe 2/3), but unless I was spending days on the phone it would make little difference and the buggering about has been non-trivial.
If you need to receive calls then it can get more complex/expensive, but I have never felt that need. E-mail or IM is typically enough, and even without a local SIM a text or two won't typically break the bank.
The above are suggestions that have worked for me in many countries, however they probably won't work in some places- I would guess Iran, North Korea etc., for political reasons, and places with dodgy Internet, for technical reasons.