Let's assume you can point, nod, count on your fingers, draw, smile and spit (not recommended in any "interacting with locals" situation). But while gesturing like a wild animal can sometimes surmount the language barrier, boning up on a handful of tricky and/or urgent phrases will save travellers grief:
1. Thank you: Like mama always said, manners are the glue of society.
2. How much is it? Sadly, not all foreign taxi drivers understand that manners are the glue of society. To avoid scams always check prices in advance (ditto for hotels, restaurants, souvenir shops, and so on).
3. Chicken/beef/pork: If you are a meat eater, learn these staples in order to identify them on an intimidating menu -- unless you fancy a surprise bowl of testicle soup. Conversely, learn the names of two "safe" typical dishes.
4. Where is the washroom? Ever heard of Montezuma's Revenge? This is a fire you don't want to play with.
5. Departures: You can afford to futz around at a restaurant, hotel or attraction, but when your train/plane/bus/ferry is about to lurch away in a matter of seconds, you need to be able to distinguish between the sign that says "departures" and the one that says "arrivals."