I've traveled to, and lived in, the developing world for many years, and I have a pretty good strategy that has worked. Overall, I try not to be paranoid about it, and I also try to keep in mind that most hotels and restaurants will go to great lengths to avoid getting visitors sick. (These days, people post reviews or blog about their travel experiences, particularly the bad ones, and a string of bad reviews from tourists could kill a business.) So, most of my rules deal with the kinds of things that are beyond the facility's control, like tap water quality.
Here's my list for higher-risk countries:
1) BOTTLED WATER ONLY - for drinking and brushing teeth - if possible, I try to find the local brand that is owned by Coca Cola or Pepsi or another major company. These days, many reputable brands will put their international purity certifications on the label as well.
2) No lettuce or other veggies that cannot be peeled. It is tough after a few days when you really want to eat a big leafy salad, but it's not worth the pain it could cause. Just want until you get home.
3) No berries or fruits that cannot be peeled. I also avoid fruits with thin, edible skins like apples and pears. Most countries have delicious fruits that have sturdy peels.
4) No street food or market stalls. Always go to restaurants that have international ratings and reviews online, and make sure there are lots of people eating there, so food must be prepared to order. Avoid restaurants that are empty, as food could have been sitting out in the kitchen, exposed to the air, for some time, and perhaps attracting insects. Also avoid restaurants with a strange or bad smell in the air.
5) Hot food should arrive to the table piping hot. If it arrives lukewarm, send it back.
6) When ordering beverages in a restaurant, ask for your water/soda in a sealed bottle. At minimum, make sure the waiter cracks the seal in front of you prior to pouring into a glass. If you can't be sure it was a sealed bottle (i.e. no seal cracking sound when waiter opens the bottle), ask for a new bottle. Some restaurants might try to save money by refilling bottles and hoping customers won't notice.
7) Pepto Bismol is the way to go for GI symptoms. Occasionally, I will chew one proactively on the first day in a new place as my digestive system adjusts. But PB is better than anything else, and it is not an antibiotic so there is no risk of killing probiotics or developing resistant strains.