Adjusting Pieces. Players may adjust off-center pieces on the chessboard (their's or the opponent's), but must do so on their turn, and must first clearly say the word "adjust".
Calling Check. Calling check is not required, although traditionally regarded as a courtesy.
Chess Clocks. Black begins a game by starting the opponent's clock. During the game, players should follow the habit of making a move, and then immediately hitting the clock with the same hand. Players are not required to remind an opponent to hit the clock, nor do they need to wait for the opponent to hit their clock before making a move (assuming the opponent has already moved). Under certain circumstances it is important to know how to stop the chess clock. Note that bathroom breaks, phone calls, etc are not legitimate reasons to stop the chess clock.
Black Chooses. Black, as compensation for moving second, has the right to choose which chess set and clock to use, as well as whether to place the clock on the right or left. One exception: if black wants to use an analog clock, but white prefers a digital clock, the digital clock is used.
Sportsmanship. In tournaments, chess players, in the spirit of good sportsmanship, traditionally shake hands and wish each other well before starting a game. Players should also respect their opponents during games by refraining from unnecessary talk or noise (please turn cell phone ringers off!). The only words that really ever need to be said during a game are "draw?" (draw offer), "adjust" (before adjusting pieces), "checkmate" (who can resist?), "time" (win on time), and "let's ask the Tournament Director (TD)" (in case of problems or disputes). After a game ends, regardless of the result, both players should continue to show courtesy by (quietly) offering each other complementary or encouraging words.
Recording the Game Result. Immediately after each game ends, the winner (or either player in a drawn game) should record the result on that round's posting sheet (but please don't write on the tournament chart). This allows the TD to prepare the next round's pairings on time.
Byes. If any round has an odd number of players, the lowest rated player among the lowest scoring group of players sits out the round and receives a full-point bye (equivalent to a win), assuming that the player has not already received a bye in the same tournament.
Spectators. Spectators are welcome to observe games in progress as long as they do not distract the players or influence the games in any way (i.e., by talking, reacting to moves, reminding players to hit the clock, pointing out that a player has run out of time, etc).
Resolution of Disputes. If a problem or dispute arises concerning a game in progress, both players should remain calm, immediately stop their clocks, and seek the TD. The TD will try to resolve the situation as fairly as possible according to the U.S. Chess Federation Official Rules of Chess.
Withdrawals. Players who withdraw from a tournament should inform the TD so that their names can be removed from the remaining rounds' pairings.
Also read the FIDE Laws of Chess (PDF)