Gedam is a GNOME crossword puzzle program.
Gedam game is similar to the AcrossLite program for Windows, and it can read and write the file format of that program. Consequently, it works well for doing puzzles from The New York Times.
Although there is an existing version of AcrossLite for Linux, it has several glaring problems: poor support, the use of Motif, and the lack of a clock.
When you start gedam, you need to give it the name of a puzzle on the command line. You can get puzzles from The Times if you're a subscriber.