In some countries, you need to pay to use public toilets. Be sure to keep some change on you at all times. If you're a fan of toilet paper (and who isn't?), you'll want to have some with you if you're traveling to a country that has squat toilets. Antibacterial hand gel is a good idea no matter where you're traveling.
Flushing mechanisms may be located on the floor in the form of a pedal, or above in the form of a chain that you pull. Be sure to find out how the toilet works before it becomes a problem.
If you don't speak the language, you'll want to at least be able to ask where the nearest toilet is located.
Spanish: Where is the bathroom? -- ¿Dónde está el baño?
French: Where is the bathroom? -- Où se trouve / Où est la salle de bain? or -- Excuse me, sir / ma'am, where is the toilet? -- Excusez-moi, monsieur / madame, il y a des toilettes? (More on the cultural aspects of asking for the bathroom in France)
German: Where is the restroom/toilet? -- Wo ist das WC/die Toilette?
Italian: Where is the bathroom? -- Dove sono i gabinetti?