Most chess games played at club level up to professional level are either King Pawn openings (e4) or Queen Pawn openings (d4). The two most commonly played alternatives are the English Opening (c4) and Reti's Opening (Nf3).
King Pawn openings are usually considered more tactical by nature than Queen Pawn openings, which are considered more "positional". This can be reflected by some top players; Viswanathan Anand favours games rich in tactics and he plays e4 almost exclusively, whereas Vladimir Kramnik is considered one of the strongest positional style players around, and he usually plays d4 or Nf3 (which leads to Queen Pawn style positions).
There are several common replies to e4 and d4, each of which constituting an opening system. I will list the main systems.
King Pawn defences are defined on black's first move, whereas Queen Pawn defences are signified usually by the 2nd or 3rd move, depending on what white plays.
King Pawn Openings (in order of frequency played at club and master level):
e4 c5 - Sicilian Defence e4 e5 - Open Game e4 e6 - French Defence e4 c6 - Caro Kann e4 d6 - Pirc e4 Nf6 - Alekhine's Defence e4 d5 - Scandinavian e4 g6 - Modern Defence