NFL Records - Team
The Broncos scored 606 points in 2013, breaking the record of 589 set by the New England Patriots in 2007.
Denver's 76 touchdowns beat the previous record of 75, also held by the 2007 Patriots.
Players with 10 or more touchdowns
The Broncos' Four Horsemen - WRs Demaryius Thomas (14), Eric Decker (11), Wes Welker (10), and TE Julius Thomas (12) - all finished with at least 10 touchdowns in 2013, while RB Knowshon Moreno added 13 of his own to break this NFL record - by two players (previous record was three).
Passing first downs
The Broncos converted 293 first downs through the air in 2013, with a small handful coming from QB Brock Osweiler in backup work. The previous record was 280 set by the Saints in 2011.
Pat Bowlen has 305 wins in his 30 years as the Broncos owner. He is the first owner in NFL History to win at least 300 games in his first 30 years of ownership.
Games with 50+ points
The Broncos had three such games in 2013, tying the NFL record that has remained untied since 1969.
Points in 2nd half
The Denver Broncos scored 318 points after halftime in 2013, beating their own record set in 2012 (299). The previous record was set in 1950 by the Rams in 12 games. (via)
NFL Records - Player
Peyton Manning finished with 55 TDs, shattering Tom Brady's record of 50 set in 2007.
Manning threw for 5,477 yards, one yard more than Drew Brees threw in 2011, the previous record. After some controversy, the NFL confirmed on January 1, 2014 that the record will stand.
Longest field goal
Matt Prater booted a 64-yard field goal in Week 14 to break the long-standing NFL record of longest field goal. That record was previously held by Jason Elam, among others.
Matt Prater went 75-of-75 for the season, setting the records for most extra points, most extra points attempted, and most extra points without a miss, previously held by the Patriots' Stephen Gostkowski in 2007 (74-of-74).
Most four-touchdown passing games
Peyton Manning destroyed this record with nine such games this season. The previous record was six, set by Dan Marino in 1984 and tied by Manning in 2004.
Most two-touchdown passing games
Manning had 15 such games in 2013, tying Marino's 1984 season.
Most 400-yard passing games
Manning tied the record set by Dan Marino in 1984 with four 400-yard passing games this season.
Most 90+ passer rating games
Manning had 15 such games in 2013, tying the NFL record he set in 2004. Stretching back into 2012, Manning decimated the record for most consecutive 90+ passer rating games in the regular season with 23.
Franchise Records - Team
In addition to the NFL records above (those are all franchise records too, of course), this Broncos team broke a handful of franchise records too. Let's break it down.
Points in a game
The Broncos scored 52 points against the Eagles in Week 4, breaking a franchise record that had stood for 50 years.
Regular season winning percentage, coach
John Fox holds a 34-14 regular season record as head coach of the Denver Broncos (.708) surpassing Mike Shanahan's franchise mark of .616.
Plays from scrimmage
In 2013 the Denver Broncos ran 1156 plays from scrimmage besting their franchise high of 1152 in 1985.
In 2013 the Denver Broncos gained 435 first downs besting the previous franchise mark of 383 in 2000.
7,317 yards is the new franchise mark set this year besting the old mark of 6554 gained in 2000.
Average per Play
The high octane offense led by the Manning passing attack managed to gain 6.3 yards per play besting the 6.21 yards per play mark set in 2008.
Most points in a quarter
Franchise Records - Player
Broncos Playoffs 2013-2014
Everything we know about the Denver Broncos' 2013-2014 NFL playoff berth, including game time and possible opponents for their Divisional Round game January 12th.
Touchdowns by a tight end, season
Julius Thomas hauled in 12 touchdowns on the season, breaking Shannon Sharpe's franchise record of 10 touchdowns in a season for a tight end. Thomas broke the record in Week 14 against the Titans.
Receiving touchdowns, game
Against the Kansas City Chiefs in Arrowhead, Eric Decker became the only receiver in Broncos history to catch four touchdowns in a game. Previously, in 2000, Shannon Sharpe logged the 12th game in which a receiver caught 3 touchdowns in a single game.
Receiving touchdowns, season
Demaryius Thomas tied the franchise record for most receiving touchdowns in a season with 14. The mark was set by Anthony Miller in 1995.
Right guard Louis Vasquez played in every offensive snap for the Broncos in 2013 and did not surrender a sack. The last player to do that was tackle Ryan Clady in 2008. Vasquez played in 78 more snaps than Clady did then, breaking the record for snaps without allowing a sack in a season (though the challenge is on for Vasquez in 2014 -Clady would extend that streak several games into 2009).
Rushing, receiving yards
Running back Knowshon Moreno became the first player in franchise history to gain over 1,000 yards rushing and 500 yards receiving.
Peyton Manning set the franchise mark for most completions in a single season with 450.
Manning also set the franchise mark for most attempts in a single season with 659.
Manning shattered his old franchise mark of 105.8 by posting a mark of 115.1 in 2013.
Interception percentage (career)
Manning has thrown 21 interceptions over the course of 1242 attempts giving him an interception percentage of 1.69 besting the mark of 1.8 set by Hugh Millen in 1994-95).
Most consecutive games with a TD pass
Manning has played 33 games as a Bronco and has thrown a touchdown pass in every single one of them. Brian Griese held the previous mark with 23 consecutive games with a touchdown pass.
Completion percentage, game
Peyton Manning finished the 2013 season by completing 25 of 28 pass attempts, an 89.3% completion rate that eclipsed all other Broncos QB's, minimum 28 pass attempts. That ranks 2nd in NFL history to Rich Gannon (34 of 38 for 89.5%, 2002).
Field goal percentage
Matt Prater set the record for highest field goal percentage in Broncos team history. By making 25/26 kicks, Prater made 96.2% of his kicks.
50+ yard field goals
Prater was in a logjam tie with five kicks made from 50+ yards when he broke the tie and booted a 54-yarder. That also made him 6/7 from 50 and beyond which sit a new high mark for conversion percentage (85.7%).
With 75 PAT's and 25 FG's, Matt Prater scored 150 points on the season besting the franchise mark set by Terrell Davis in 1998 (138 points).
Career winning percentage, quarterback
With a two-year mark of 26-7 (.788), Peyton Manning surpassed Jake Plummer (39-15) as the franchise leader in winning percentage by a starting quarterback.
Most passing attempts, game
Manning threw the ball 59 times against the Tennessee Titans tying the franchise mark set by John Elway in 1993.
Big thanks to Bronco Mike for helping me compile this list. Big thanks to our readers and commenters for adding more to this list! Let us know if we missed any 2013 Broncos records in the comments!