1. The pattern of black-and-white squares must be symmetrical. Generally this rule means that if you turn the grid upside-down, the pattern will look the same as it does right-side-up.
2. Do not use too many black squares. In the old days of puzzles, black squares were not allowed to occupy more than 16% of a grid. Nowadays there is no strict limit, in order to allow maximum flexibility for the placement of theme entries. Still, "cheater" black squares (ones that do not affect the number of words in the puzzle, but are added to make constructing easier) should be kept to a minimum, and large clumps of black squares anywhere in a grid are strongly discouraged.
3. Do not use unkeyed letters (letters that appear in only one word across or down). In fairness to solvers, every letter has to appear in both an Across and a Down word.
4. Do not use two-letter words. The minimum word length is three letters.
5. The grid must have all-over interlock. In other words, the black squares may not cut the grid into separate pieces. A solver, theoretically, should be able to proceed from any section of the grid to any other without having to stop and start over.
6. Long theme entries must be symmetrically placed. If there is a major theme entry three rows down from the top of the grid, for instance, then there must be another theme entry in the same position three rows up from the bottom. Also, as a general rule, no nontheme entry should be longer than any theme entry.
7. Do not repeat words in the grid.
8. Do not make up words and phrases. Every answer must have a reference or else be in common use in everyday speech or writing.
The above rules apply to the crosswords in almost all publications. The New York Times' Crossword Specifications sheet lists some more special rules of The Times.
Note: "Random House Puzzlemaker's Handbook" by Mel Rosen and Stan Kurzban (out of print, but widely available in libraries) contains detailed advice on creating and selling crosswords. This is an excellent starting point for new constructors.
(this document provided by Will Shortz, editor, New York Times crossword puzzle)