Combining some of the comments to the previous answer, and contrasting the accepted answer, some board and card game mechanics can be patented as well as the content (art, instructions) being copyrighted/trademarked.
There's a fine line to draw, but also a relatively simple rule of thumb. Basically, if you can find an example of a game that uses the mechanic which was documented as being played prior to the ratification of the United States Constitution, then the game and any mechanic it has at that time are not eligible for patent, and you have an excellent case for moving forward with a game using the mechanic, whether you find a filed patent or not.
This "public domain" rule encompasses a lot of the basic mechanics that people know and love:
- Pretty much every board game involving a regular grid constraining the directions and limits of movement of pieces, regardless of the shape of the spaces or the lines, drawn or implied, connecting them.
- Maps of real geographic terrain, including pretty much any "projection" of the world as a map (you can't use actual prints from mapmakers - they're copyrighted - but the shape of the earth, and the names of cities, states, provinces, countries, and continents belong to no man or corporate entity)
- Jumping one piece over another and landing in an adjacent space in line on the other side (draughts, Dai Hasami Shogi, countless others)
- Capturing a piece by moving into the same space on the board (Chess, countless others)
- Stacking pieces to indicate rank (draughts)
- Having various pieces with different roles, movement or capturing rules (Chess, Shogi, draughts variants such as Dablot Prejessne, countless others)
In addition, if a game mechanic was first shown in a game more than 20 years old, and the mechanic was patented, the patent has almost certainly expired and is now in the public domain as well. If it was developed and widely used more than 20 years ago, but never patented, you can generally make the same claim. Until 2011, patent law was based on a doctrine of "first to invent", meaning that if you could prove someone else had the idea first, you could get any patent filed after that date invalidated in court. This is what happened to Apple when it sued Microsoft for infringements of patented design elements of the Apple Macintosh; it turned out that Apple had first gotten the ideas from Xerox, who was therefore the "first to invent" and Apple's patents were void.
However, patents filed since 2011 are based on a "first to file" doctrine, meaning that in order to invalidate a patent, you have to prove the idea was overtly released to the public domain prior to the filing date, and so simply proving someone else thought of it first is insufficient; you must prove that they thought of it and made some overt action releasing the IP for general use. If all of the Apple and Microsoft startup stuff had happened in the last 10 years, and Apple v. Microsoft were to be heard this year, Microsoft would be in a world of hurt because Xerox, who never patented the ideas they let Apple use, would have nothing to say about Apple having filed the patents. So, if it's a relatively novel game mechanic, seen for the first time in a game released in the last couple of years, be very careful.