The Giants were originally known as the Gothams and entered the National League in 1883. 

The famous Giants player-manager, John McGraw, managed the Giants for three decades. 

One of the most famous moments in Major League Baseball history was known as “Shot Heard ‘Round The World” when Giants’ slugger Bobby Thomson hit a walk-off homerun off of Brooklyn Dodger’s pitcher, Ralph Branca, on October 3, 1951. You may have heard the famous call from announcer Russ Hodges after Thomson launched the shot – he shouted “The Giants win the pennant! The Giants win the pennant! The Giants win the pennant!”

The Shot Heard 'Round The World

The Catch”, an amazing over-the-shoulder grab made by center fielder Willie Mays of the Giants, occurred in game 1 of the 1954 World Series. The Giants went on to sweep the Cleveland Indians in 4 games despite the fact that The Tribe won 111 games in the regular season. This was the last World Series Title for the Giants until this year’s defeat of the Texas Rangers.

The Catch

In 1957 the Giants moved to San Francisco and the Dodgers moved to Los Angeles. Both teams moving west the same year was not a coincidence because The Dodgers’ owner, Walter O’Malley, was told that the Dodgers couldn’t move to LA without another team coming to California. In essence, O’Malley put some pressure on Giants’ majority owner, Horace Stoneham, to head to San Francisco.

The Giants played ball at Candlestick Park for 40 years, then moved to what is now known as AT&T Park in 2000. The park sits on the shores of the China Basin, which is commonly referred to as McCovey Cove by Giants fan.

In 2002, the Giants and Angels both entered the post-season as wild card teams. They ended up playing in the World Series, marking the first time two wild card teams played in the World Series. The Angels defeated the Giants in an exciting 7-game series.

The Giants defeated the Texas Rangers in this year's World Series. It was the first trip to the World Series for the Rangers. 

To date, the Giants have 21 National League Pennants and 6 World Series Titles.

References:

http://en.wikipedia.org/wiki/San_Francisco_Giants#New_York_Giants_history

http://www.huffingtonpost.com/2010/11/01/giants-world-series-champions-2010_n_777417.html