Infinite chess is a variant where the board expands infinitely in all directions. It can lead to some funny moments by moving your queen really far away than moving around and attacking the king from millions of squares away. It can be found by searching up "infinite chess" on Google. It is not a variant on chess.com or lichess.org.

Atomic Chess

A variant where capturing a piece causes every piece adjacent to it, except for pawns, to also be taken, even your own pieces. This also applies to the king so be careful about pieces right next to your king. This variant is available on chess.com and lichess.org

Fog of War

A variant where all your opponent's pieces are invisible to you. Any pieces occupying the squares that your pieces can move to will be visible. This forces you to make sure your king isn't exposed or else your king might be captured without you knowing. This variant is available on chess.com.

Three-Check

A variant where the normal rules apply but getting three checks against the king will automatically result in a win. This also forces you to protect your king more. This variant is available on chess.com and lichess.org.

Antichess

Unlike normal chess, the goal of antichess is to give away all of your pieces. There are no checks or checkmates. If you can take a piece, you must take it. If a stalemate occurs, black wins automatically. This variant is available on chess.com and lichess.org

Chess 960/Fischer Random Chess

Every piece on the 1st and 8th rank will have their positions randomized. Castling is slightly different in this variant because the rooks and kings could be on the other side of the board or right next to each other. The positions of the pieces are mirrored on each side. The pawns are unaffected. This variant is available on chess.com and lichess.org

King of the Hill

A variant where standard chess rules apply. The only new thing is that if the king enters one of the four central squares, that side automatically wins. Your king cannot enter the center if the square is being defended. This variant is available on chess.com and lichess.org

Crazyhouse

A variant where you can place pieces that you captured back on the board. Kind of like forcing the enemy pieces you captured to fight for you. You cannot place a pawn on the 1st or 8th rank and you can only place the piece on an open square. This variant is available on chess.com and lichess.org

Bughouse