We've been on the road for 15 months in Asia (Caucasus, Central Asia, China, Southeast Asia, India) and spent a lot of time traveling in Western/Central Eastern Europe beforehand. We have been able to use ATMs and local currency for the most part. We've been surprised to find ATMs in some obscure places.
However, there are times when USD is required - visas come to mind, as do hotels in certain parts of the world (eg, Uzbekistan). Euros are becoming more accepted and desired in some areas, so it's pretty easy to change Euros as well in most places. But, I agree that there are some countries that still have an attachment to the $, even as it is declining by the day.
There are some countries that give you a choice of currency at the ATM machine so you can take out USD or local currency - Georgia, Azerbaijan, Cambodia come to mind. There are also countries without ATMs - Turkmenistan, Uzbekistan (except for 1 or 2 in 5* hotels in Tashkent), Burma/Myanmar where having a stash of USD is absolutely necessary.
We started our trip with a stash of USD and Euro in our money belts and have restocked in countries where we can get it from the ATM or have exchanged local currency from an ATM for $.
