King in the Center
Miniatures (games concluding in less than 25 moves) are often the result of one side leaving the king in the center. Sometimes you can delay castling, but if pawns are exchanged in the center you're better off scooting to safety as quickly as possible.
This example is actually known to Opening Theory as my opponent makes a mistake against the Sicilian and finds himself overrun.
The second example is a bit trickier and both kings were in a bit of danger before the knockout blow.