Any live cell with < 2 or > 3 live neighbours dies due to loneliness or overcrowding.
Any live cell with 2 or 3 live neighbours remains alive.
Any dead cell with exactly 3 live neighbours becomes a live cell.
Examples:
Acorn, b-heptomino, die hard, pi, r-pentomino, thunderbird etc are examples of methuselahs, patterns that take a large number of generations to stabilize.
The beacon is a period-2 oscillator.
The blinker is the smallest and most common oscillator.
The dart travels across the board at a speed of c/3 (one cell every three generations).
The figure of 8 is a period-8 oscillator.
The glider travels diagonally across the board at a speed of c/4 (one cell every four generations).
Gosper and Simkin glider guns emit gliders repeatedly.
The light, medium and heavy spaceships travel across the board at a speed of c/2.
The loafer travels across the board at a speed of c/7.
The pentadecathlon is a period-15 oscillator.
The t-tetromino stabilizes as a traffic light (4 blinkers).
The tumbler is the smallest known period-14 oscillator.
Below are a few common Game of Life Still Lives and Oscillators: