Most importantly, know where you are going; the place, customs, people. Know that if you go to Istanbul and want to visit a Mosque that they expect women fully covered whether you are a tourist or not. Things like this are important if you don't want to offend the people, and in turn, maybe cause yourself a problem. You might not get to do something simply because you didn't know something was expected of you. Ignorance is not really a good excuse.
If you take multiple trips, Try one self planned, and then another one that is a tour. The experiences are so different, and both are awesome!
Pay attention to where you are and where you're going. Being lost in a different country where you might not even be able to read a street sign sucks... Been there lost in France for a few hours once, and I wasn't even in a difficult area to navigate; it was just Super late and very dark.
Careful with anything water related you drink, or eat. The organisms in the water where you live are different than where others live. You can make yourself really sick and ruin your trip. Buy filtered water, boil your own, etc. Don't eat random fruit, they are grown with the same water.
Learn some of the language if you can wherever you go, know where an embassy is, what number to dial in an emergency. Even learning the alphabet can help you read a map or a street sign to know where you are.
Definitely check the climate of where you are going and at what time of the year you are going. You don't want to be in winter clothes is it's 100 degrees outside, or a bikini if it's 40 lol. Is it humid? Do you need bug spray? Do you need shots for the country you are visiting?
Do be surprised by the fact you might see some weird customs; some that may even offend you. You are in their world now and it might be everyday kind of stuff for them. Might even be worth trying? Are you adventurous?
The touristy stuff can be super awesome! Even if it's full of a bunch of tourists and cliche. Don't not do something just because everyone else is doing it. And yes, get out and see that uncommon things.
Meet the locals. Ask for suggestions! Some of the best places i've eaten, stayed, hung out at, were recommended by people that live where I was visiting. They obviously know the best things in their own area.
This list can go on and on. This was just to touch on a few off the top of my head :) @missy & @rambo