Do all companies pay Dividends?

No.  Some companies pay dividends while others do not.

For example, Coca Cola (NYSE: KO) pays dividends four times per year (Source: Coca-Cola's Dividend Schedule).  Coca Cola has paid a dividend each year since 1920 (Source: Coca-Cola Owner's Guide)

Apple, Inc. (NASDAQ: AAPL) pays them VERY rarely (and never while Steve Jobs was in charge), instead opting to retain their earnings for future use.  This strategy led to a point where during the summer of 2011 Apple, Inc. had more cash ($76.2 billion) than the United States government ($73.77 billion)!  (Source: CNNWall Street Journal).

Other companies do not pay them at all.  Berkshire Hathaway (NYSE: BRKA) has never paid a dividend, instead reinvesting their profits.  It's hard to argue with Warren Buffet's plan however.  In July of 2012, the stock of Berkshire-Hathway was selling for over $125,000 FOR ONE SHARE.