Bernie Kosar 308
(this is not the answer. Kosar had the most ATTEMPTS without an interception, not the most completions. And Tom Brady broke this record on 12/26/2010)
His bio on steelers.com claims that Charlie Batch had 145 consecutive completions without an interception when he was with the Detroit Lions. Given that Tom Brady's current record for pass ATTEMPTS without an interception is in the 300's (as of 12/27/10), 145 completions sounds as if it would be close to the record. I don't know if it is the actual record, though. Can anyone find a QB with more?
Otto Graham of the Cleveland Browns started 6 consecutive NFL Championship Games between 1950-1955.
Reggie McNeal, Texas A&M
Orlovsky
The most consecutive starts was by Jim Kelly of the Buffalo Bills who started 4 in a row (SBs XXV through XXVIII).
Check out the 'Consecutive Games Played Streaks' link on this page to see the 15 longest consecutive games played streaks in MLB history.
Drew Brees
Jay Fiedler
Roger Staubach
Dan Fouts had 45 consecutive games with 200+ passing yards from 1980 to 1983
Drew Brees
Otto Graham of the Cleveland Browns started 6 consecutive NFL Championship Games between 1950-1955.
Rich gannon
Tom Brady
Reggie McNeal, Texas A&M
Orlovsky
Brett favre
Terry Bradshaw