That depends on what league, and what season is currently playing.
For the NFL, regular season statistics:
2002: Chad Pennington
2003: Steve McNair
2004: Peyton Manning
2005: Peyton Manning
2006: Peyton Manning
2007: Tom Brady
2008: Philip Rivers
2009: Drew Brees
2010: Tom Brady
Please see the related questions below for more specific answers, for instance by season, or for all time.
Tom Brady with a rating of 111.
Aron roger
Drew Brees
As of this posting it's Michael Vick with a rating of 108.7
Using quarterback rating, through the 2007 season that would be Steve Young who had a career quarterback rating of 96.8. Peyton Manning is second all time at 94.7 and Kurt Warner third at 93.2.
Thru week 8 of the 2008 season (not counting the 10/27/2008 MNF game), San Diego Chargers quarterback Philip Rivers has the highest passer rating in the league. His current rating is 107.8. He is followed in the passer rating standings by Tony Romo (Cowboys) - 103.5 and Kurt Warner (Cardinals) - 102.1.
88.5
98.6 quarterback rating.
Trent Dilfer
Aaron Rodgers
The best quarterback of the 2009-2010 NFL season was Drew Brees of the New Oleans Saints. He led them to their first super bowl victory, and held the best quarter back rating and led touchdowns for the season as well.
In 2009, Eli Manning had a 93.1 quarterback rating.