You can find a host of interactive puzzles and games online. The popularity of programs like Adobe Flash has given rise to an enormous number of websites devoted entirely to games animated by freelance designers and graphic artists. One example of such a site is Newgrounds.com. You can play games of almost every conceivable genre and, if you sign up, you can earn points for reviewing the games and acquire access to special features. Other examples include Miniclip.com and Armorgames.com.
The games section of each site has a specific category devoted entirely to puzzles, and the medium of Flash animation has allowed developers to be extraordinarily creative with the type of games they design. You can play sudoku, word searches, murder mystery puzzles, sliding block puzzles and "escape the room" puzzles (where you are locked in a room and have to combine items to devise an escape plan).
Be advised, however, that not all content is child-friendly. Anything of a slightly more adult nature is clearly marked as such.
Venerable strategy games like chess and checkers have also acquired a substantial online presence. At Chess.com or Gameknot.com you can register an account and either play against a computer or against other users, including some genuine grand masters. You can also solve and create your own chess problems.
You can play number puzzles like sudoku online as well. The site Dailysudoku.com offers a new sudoku puzzle every day. It also has a special section of sudokus designed for children.
Ken-ken are similar puzzles with a slightly higher emphasis on arithmetic than a traditional sudoku. In a Ken-ken, the solver is presented with an empty 9-by-9 grid which is subdivided into irregularly shaped sections. In each section is a number and a mathematical sign such as 11 + or 4 -. These are target numbers. The goal is to fill the grid with the numbers 1 through 9 while making sure that no digit appears twice in each row or column. Also, the solver must use the numbers in each irregularly shaped section, along with the mathematical sign, to create the target number. For example, all the numbers in an 11 + section must, when added together, total 11. You can find examples on KenKen.com
If you don't want to solve online you can also find books on recreational mathematics at your local library. Perhaps the best known math puzzle creator was Martin Gardner, who wrote dozens of excellent mind-bending books of original math puzzles that will leave all but the most dedicated mathematicians scratching their heads.
You can find crossword compilations at any good bookstore or library. Crosswords can be divided into two categories. The first is general knowledge and the second is cryptic. Cryptic crosswords feature clues that function as small, self-contained riddles. They tend to be far more intellectually challenging than traditional general knowledge crosswords but are also very popular because, while the clues themselves may be difficult to decipher, the solutions are generally commonplace words. Cryptic clues rely on anagrams, double-meanings, puns and homonyms and also appear in most daily newspapers.
You can find both types of puzzle on-line at Crosswordsite.com.