In most regions of the world you will not have a hard time finding decent food since local and international choices are widely available. With a little effort such as asking other travelers, the locals or consulting your guidebook you will probably find the best and cheapest deals in the narrow streets away from the tourist spots. If you fancy the local food, always go for the places where the natives eat.
When traveling on a budget, you will most likely stay out of the most expensive eating places, although once in a while you should treat yourself to a feast. Eating on the cheap may foster a few hiccups with your stomach, but this is part of the backpacking adventure and most travelers experience some sort of light diarrhea when traveling for longer periods abroad. Make sure to take your precautions, eat your vitamins and always drink bottled water - and lots of it. Also wash your hands (or use dry wash gel/antibacterial liquid) and if you stick to the old philosophy of "boil it - peel it - cook it, or forget it", you will most likely be safe and sound, but then you will have to stay clear of much of the local cuisine and snacks - and that's really not explordinary, is it?
In some parts of the world the local language menu card will be a challenge - there may not even be one at all and you will have to do the "close-my-eyes-and-point" trick or look/ask around for your favorite choice of meal. It's an exciting game, so at least get acquainted with the most common dishes in the area you are visiting, bring a phrasebook or look it up on your smart phone. Vegetarians will have to work a bit harder and the menus and choices will be limited in some parts of the world, but you should be able to get by in most countries.
In most developing countries drinking water does not come out of the tap. If you want a risk free adventure always drink bottled water - and if it's not available, take precautions by using some sort of water purification chemical or a portable water filter before drinking the water. Same goes for drinking water from streams, rivers and lakes, always boil it well and use a water filter or purification chemicals.
When traveling rough and on the wild side, make sure to eat and drink regularly, never start skipping meals and avoid too much junk food. It may seem like basic advice but it will help you to keep a balanced diet throughout your journey.