Pocket Corkscrew -- carry-on allowed by TSA (because there is no blade) in Canada and the US, but reportedly will be confiscated in Europe.
Had one for years that lived in my bathroom kit, loaned it out once while travelling and never got it back. Searched far and wide before finding another (albiet pricier) TSA approved corkscrew.
Hotels giving out the first one are cool, but giving out the 2nd one pictured would be absolutely fabulous!