I am traveling internationally, should I avoid tap water for fear of e.Coli contamination?

Possibly. This will depend on what country, and sometimes what region within a country you are traveling to. Undeveloped countries typically have higher rates of water contamination, which increase a traveler's risk of getting an infection (e. Coli, viruses, etc.) this not only applies to what you drink, but also to foods washed in this water, ice cubes, etc. Bottled water that you unseal is safest.
Traveller's Diarrhea. When traveling, it is always a good idea to avoid local tap water and food prepared by washing, such as salads. Pepto bismol (bismuth subsalicylate) tablets or liquids area great way to "prepare" the gut for any microbial assault. Drink bottled beverages and be vigilant.