Lighters and breastmilk can be brought on board. Strange combo? But seriously, the TSA has confiscated millions of lighters and has gotten into some hot water for confiscating the pumped breastmilk of mothers who have had to travel for business or whatever other reasons without their infants - and pumped breastmilk takes time and energy and should never have been banned as carry on since it could easily be spoiled in checked luggage.
It's important to note that depending on the country you travel to their may be some differences in what you can bring on board, which are highlighted below.
In the U.S. corkscrews are allowed for carry-on, whereas in Canada corkscrews are only permitted in checked luggage. Toy weapons are banned as carry on in the U.K., Canada, and other countries, but only true-looking replicas are banned in the U.S.. Metal nail files are nearly universally banned, but nail clippers with no metal nail file are not.
Any doubt of what you can or can't bring can be taken away by following the links to some of the government websites about airport security screening. Any further doubts? Then it is a good idea to call the airline directly as they will outline what can/not be brought on board, and can advise you not only about banned potential weapons, but about what the airline considers dangerous goods as well.