Conditioner: I found this conditioner while in college and bought a bottle specifically for this trip. It smells nice and tropical-y while making my hair really shiny and smooth. A deep conditioner is essential for travel because different environments can make your hair act weird. The differences in water between countries can really mess with your scalp-- when I moved to Singapore, my hair fell out for months getting used to it. A really good conditioner can make the difference between impossible to deal with hair and hair that actually looks okay in photos.
Comb: I find my peach-wood comb essential for everyday styling and detangling. I'll talk more about wood combs in another post, but wood combs are awesome.
Boar-Bristle Brush: I've only recently started using this every day, but I think it's worth bringing. I like brushing my hair because it adds shine, detangles and gets rid of fly-aways.
Some other things I am bringing that are not pictured above: hair bands and bobby pins. That's it!
Wait a second... there are a few things that you may have noticed I did not include:
Shampoo. At least with me, it doesn't matter what shampoo I use. It's all about the conditioner.
Hair dryer. I've been to several 3rd world countries, and 99% of the time I have been able to find a hair dryer somewhere. I don't actually use hair dryers, but it's nice to know that most places have them.
Hot styling tools. Unless you are sure you know your tools work outside the country and you cannot live without them for some reason, leave them at home. Not only do they damage hair, but who knows how your hair will react in a different environment anyways? Those curls you spent half an hour working on may go flat in the humidity, or worse, frizz beyond saving.