For example, did you know that the "first-move advantage" in chess that goes to White has been debated for a long time whether it even exists? While the current prevalent idea is that against an equal opponent you should expect to win as White and draw as Black, this is far from universal and has been debated for a long time. If White does have an advantage, it only comes out to about 2 to 6% more won games.
Here's another link on cheating in chess, most of which is either getting help from outside sources (meeting them in the bathroom, sneaking looks at a handheld computer, etc.) or touching a piece and not moving it.
Another link on world records in chess. The "worst performance in simultaneous games" is pretty amusing, with Robert Wade losing 20 out of 30 games, including one to a seven-year-old.
Underpromotion (promoting a pawn to anything other than a queen) is very rare, but does occur in certain very specialized circumstances. It usually happens when promoting the pawn to a queen would result in a stalemate.
Antichess is a cool chess variant where both sides try to lose all their pieces first, and kings have no special powers (no "checking" occurs). Players must capture a piece if it is possible.
Some other clever chess variants exist. Chess boxing is alternating rounds of chess and real boxing, with victory possible via knockout or checkmate. Chess960 was created by Bobby Fischer that randomizes the back rank of pieces. There are other really cool variations that seem real fun to play too- for example, using different numbers of starting pieces or capturing rules.
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