They will occasionally pilfer thru your checked bags without you present. I've seen several little flyers in my luggage after I get home attesting to and explaining the search.
Security checks and rules do seem to vary, and I don't know if that's due to incompetence or intentionally changing things up to keep the terrorists on their toes.
I've gotten the impression they generally don't like matches, but carried in a pocket they won't likely be noticed, and if noticed they just take them away. But my wife carries a Bic lighter on board without hassle, and my full-size Zippo merely gets lit at worst to verify that it's not a disguised .22 pistol (for real!). I don't recommend lighters in checked luggage, as they do not like any kind of fire hazards in the airplane compartments.
I can't comment on cutters, although I've "heard" they're ok lately, so I either check them, or pre-cut cigars for short, carry-on luggage trips.
I have considered carrying a largish self-addressed and overstamped (?) envelope in my carry-on, in the event that I forget and carry my pocket knife, etc; any valued "contraband" could be dropped in an airport mailbox. There are usually mail drops around there somewhere.