What do you take while travelling or what is really necessary?

The costs of flying with your luggage is increasing. This website gives you the baggage fees for the top ten airlines:  http://budgettravel.about.com/od/airfarescruises/tp/majors_bagfees.htm
For instance, American Airlines charges for flights within the U.S., Puerto Rico, and U.S. Virgin Islands, $25 for their first checked bag and $35 for the second bag. One carry-on is permitted at no charge.

The beginner's guide to Minimalist Travel gives these pointers for getting by at a cheaper rate:
http://zenhabits.net/the-beginners-guide-to-minimalist-travel/
1. Use a smaller carry-on.
2. Pack neutral colors and no more than 3 shirts for an extended trip.
3. Multi-use soap cuts down on liquids.
4. Wash clothes in sink.
5. Buy it during your trip and ship extra stuff home.
 
Pointers on how to travel as a minimalist:
http://articles.sfgate.com/2008-07-20/travel/17173951_1_laundry-packing-shoes
1. Make 2 piles: one for items you need and another pile for stuff that would be nice to have, then place the first pile in your suitcase and the second pile goes back in your closet.
2. Wear a pair of shoes and bring 1 pair of shoes.
3. Bring fewer clothes and wash them in the sink or use a drop-off laundry.
4. Bring 1 luxury item: a lightweight robe or and ipod which can double as a PDA.
 
Miss Minimalist: Living a beautiful life with less stuff. Her objective, was to pare down her luggage to the size of a large purse. Read about how she does it here:
http://www.missminimalist.com/?p=880