what sort of items are you not allowed to bring with you on an airplane?

The details are quite clear on the TSA website - and not as stated by others in answer to this question.

For departures from US airports, the rules are listed on the TSA website here:

http://www.tsa.gov/311/311-carry-ons.shtm

Simply stated, all liquids, gels, pastes, lotions, creams, aerosols and other similar items must be in containers that hold 3.4 ounces (100 ml) or less. All such containers must be able to fit into a 1 qt. zip lock type bag. If you try to take a container that holds more than 3.4 ounces, then you will be told to discard it. You cannot take a 6 ounce container that is half full. The TSA people will not debate you about how much is actually in that container. It will be discarded.

If you want to take more items than will fit into 1 bag, or to take larger quantities, then they can go into a checked bag.

There are exceptions to the liquid rules for medicine and medical items.

If you want much more detail, please read the information on the TSA web site: http://www.tsa.gov/

That will provide as much information as you care to read about.

Yes they will. My mom had her hairspray taken away because it was in those big cans and never got it back. Good hairspray too....

Also : you are not allowed to bring anything over 3 ounces. You can of course bring crackers and stuff. Just not Hand Sanitizer, hair spray, etc.

You can't bring more than 2.5 ounces of liquid. Basically, no liquid. No deodorant (mostly) toothpaste, shampoo, drinks, alcohol, etc etc. If you are flying in another country, you cannot bring good and stuff from that country.