The FIRST thing you have to do is remember to take your PASSPORT! This may seem obvious but when you are anxious and in a hurry you may easily forget it. I have almost done that a few times! Obviously you won't get very far, but you don't want to have to go all the way back home to get it. Be sure to check before purchasing your ticket whether or not you need a visa to travel to the country you plan on visiting! Otherwise you won't get in!
Second, you need either cash and/or a credit card. I never travel with a credit card, just because you get charged international fees to use it which is not worth it to me. But, a credit card can be in case of emergency so it is good to have with you. Cash is easier for me, I can easily keep track of what i'm spending; which I like because I usually have a budget on my trips. Make sure you have already changed your local currency to the one in the country you are travelling to. This makes it so much easier because you don't have to look for places to exchange your money. While you are exploring do not bring all your money with you in case you lose your wallet or someone pick-pockets from you. Make a daily budget and bring enough money for everyday of travel plus a little more, if you are just using cash.
Also, check the vaccination requirements. To go to some countries you require you to get vaccinations otherwise you can't even get a visa. Vaccinations can be expensive so add this into your trip budget. Check this website for your destination http://wwwnc.cdc.gov/travel/destinations/list
Phrasebook/Travel book. This is essential for travelling abroad. Having a travel book is a great way to figure out what to see, where to stay and how to get around in other countries and you can bring it with you! Obviously you should do most of your research online when you are planning your trip, but this is something you can always carry with you.
If you are going to a country where English is not the first language you NEED a phrasebook. How else will you communicate with locals? Phrasebooks are great to have since they have dictionaries at the back and also different phrases to help you get directions, order food, etc. Lonely Planet has travel/phrase books for every country. Check Chapter's, Indigo, Barnes & Nobles, etc.
Itinerary. This is important to have when going on your trip. Also, at the airport customs will most likely ask you where you are going, when you are coming back and where are you staying. You need proof to show them you are coming back home after your trip or else they might not let you travel. An itinerary also have the address of the hotel you are staying at in case you are lost someone will be able to help you.
Travel Insurance. This is important for travel to foreign countries; if the airline loses your luggage, if you need to cancel the trip, you get sick, etc. you are covered and do not have massive fees to pay or have to replace all your belongings.
Next, if you are doing an international trip you might want to purchase a neck pillow. These can be bought from Wal-Mart, Target, Walgreens, Shopper's Drug Mart, etc. Neck pillows are very handy! Even though airlines supply pillows for long flights they are not very soft.
Neck pillows are made specifically for travelling and they protect your neck from getting strained if you were to fall asleep. I don't think it is necessary to bring a blanket since the airline supplies blankets on long flights.
A camera. Remember to bring a camera to document your trip. You want to have some pictures to remember your trip. You should buy a new media card, that way you don't run out of space and have to delete any old pictures on your camera. You can also just use your cellphone, but that will take up lots of memory on your phone.
Buy a universal adapter. Some countries have different outlets and plugs, so it is be a good idea to bring an adapter with you. Adapters in other countries can be hard to find especially if they don't speak English. Save the hassle of your phone and camera dying and bring an adapter with you. You can purchase these in Wal-Mart, Target, etc where you would find travel accessories.
Etiquette. It is important to be aware of the social and cultural rules where you plan on visiting. The worst thing you could do is offend people! For example, some country's think tipping is rude other country's you always have to tip. Do your research and find out what the norms are in your destination.
Also, be aware of how you dress. Try to wear modest clothing if you're not sure. Again, you don't want to offend people. In Korea it is taboo to have bare shoulders. Clothing is one of the easiest ways to offend a culture. Do your research before hand!
Lastly, an open mind. Your going to a foreign country for a reason right? To travel, to have new experiences, to meet new people....so be open. Try different cultural foods, do activities that you might never do regularly, meet locals. Don't be afraid to be adventurous in a new country!