I earned this lesson while on a trip a few months ago when the airline temporarily lost my luggage: it pays to have a small, survival travel kit that packs some essentials with you, aside from the ones you put on your check-in luggage. The kit should be small and TSA-compliant so that you can bring it to the cabin, so no liquids more than 100 ml, and no Swiss-knife type implements and scissors.
Here's what I usually put on my travel survival kit: an extra pair of contacts (and a small bottle of contact lens solution, OTC medicines such as anti-diarrheal and anti-allergy tablets, wet wipes, toothbrush and a small tube of toothpaste, grooming implements such as a small comb, Q-tips, deodorant, and a sachet or two of shampoo. I also would put a few dollar bills inside, in case of an unfortunate event of losing my wallet.
I usually carry it in a small backpack when I travel, where I pack it with other essentials, such as my phone, a book, and a charger (plus my camera). A clean pair of underwear and a shirt too can do wonders when you're in a strange country and your airline misplaces your luggage.