Carry-On
Keep your cash, travelers cheques and important documents in your carry-on bag. Other important personal items such as medication, contact lenses should also be included. If you are on a long flight with multiple stopovers having a change of clothes is a good idea as luggage tends to get lost or delayed more often on these kind of flights. A tooth brush, shaving kit, etc. is nice to have to freshen up during your stop overs.

Separate your valuables
Put your credit cards, cash, travelers' cheques into as many possible different pockets in your bags when packing. If one bag gets stolen then you may still have some other cash available in another bag. It is also a good idea to keep you travelers' cheques and their receipts separated, so in the case that your travelers' cheques are stolen you have all the receipt numbers.

Clothes
Pack only the clothes you know you will use and if you are traveling for a longer period of time plan to wash on the road. Roll you clothes, you will be able to fit more clothes into your bag if you roll them instead of folding them. Your clothes will also get less wrinkled if you roll them in tissue paper.

Shoes
By placing your shoes inside some socks and then inside a ziploc bag will help in making sure everything else in you bag stays clean and odor free. As well placing socks inside your shoes can also save some room.

Toiletries
Store your shampoo in small containers and only fill them half way. This will avoid any kind of leakage due to pressure changes while in the aircraft. Only take half a tube of toothpaste and roll it up tight. If you want to pack toilet paper for emergencies, only take half a roll and crush it so you can fold it in the middle. Plastic bags are always handy to put your toiletries in to prevent leakage and they also have many other uses.

Gifts
If you are planning on packing some gifts with for friends or family, it might not be a good idea to wrap them. You could be checked at customs and be required to open them.