I read the same advice as Graham re. Egypt....but in fact I found when I got there most Egyptians (pre-Lotus Revolution) struggled to get US currency changed. The Red Sea resorts may be different but certainly in the Nile Valley you need to get hold of low denom notes for tipping, and these were always in short supply (and filthy).
The thing is, a whole dollar isn't a big thing to us, but it's about 4 times the standard tip in Egypt. While that's lucky for the recipient, it spoils the whole shebang - other staff start mithering for more tips, other tourists get put under undue pressure, and it then becomes the expectation rather than a civilised recognition of service provided / reasonable greasing of a low-income palm.
Traders in tourist areas seemed happy to sell in dollars, euros and sterling.
So I'd suggest getting hold of low denom currency when you get into each country for local tips- and if Egypt is anything to go by, some antibacterial hand wipes.