Mobile version. Acronyms are explained below. All times Eastern and PM, except where obvious. As of 11/15/2019 02:37:09 AM -0800.

Bowls When Where Time TV Teams Predictions
Bahamas Bowl Dec. 20 Nassau, Bahamas 2:00 ESPN MAC C-USA Miami Florida Atlantic
Frisco Bowl Dec. 20 Frisco, TX 7:30 ESPN2 AAC C-USA/MAC/MWC Nevada? Marshall
New Mexico Bowl Dec. 21 Albuquerque, NM 2:00 ESPN MWC #2/3 C-USA San Diego State Alabama-Birmingham
Cure Bowl Dec. 21 Orlando, FL 2:30 CBSS AAC Sun Belt #4 Tulane Georgia State
Boca Raton Bowl Dec. 21 Boca Raton, FL 3:30 ABC AAC/C-USA MAC Western Kentucky? Toledo
Camellia Bowl Dec. 21 Montgomery, AL 5:30 ESPN MAC Sun Belt #3 Western Michigan Georgia Southern
Las Vegas Bowl Dec. 21 Las Vegas, NV 7:30 ABC Pac-12 #5 MWC #1 California Boise State
New Orleans Bowl Dec. 21 New Orleans, LA 9:00 ESPN C-USA Sun Belt #1 Southern Mississippi Appalachian State
Gasparilla Bowl Dec. 23 Tampa, FL 2:30 ESPN ACC #9/C-USA AAC Charlotte? Central Florida
Hawaii Bowl Dec. 24 Honolulu, HI 8:00 ESPN AAC BYU/C-USA Navy Brigham Young
Independence Bowl Dec. 26 Shreveport, LA 4:00 ESPN ACC #7/AAC/C-USA SEC #9/AAC/C-USA Florida State Southern Methodist?
Quick Lane Bowl Dec. 26 Detroit, MI 8:00 ESPN Big Ten/MAC ACC #8/MAC Michigan State Boston College
Military Bowl Dec. 27 Annapolis, MD 12:00 ESPN ACC #6 AAC Louisville Temple
Pinstripe Bowl Dec. 27 New York, NY 3:20 ESPN ACC #2/3/4/5 Big Ten Pittsburgh Illinois
Texas Bowl Dec. 27 Houston, TX 6:45 ESPN Big 12 #3 SEC #2/3/4/5/6/7 Kansas State Texas A&M
Holiday Bowl Dec. 27 San Diego, CA 8:00 FS1 Big Ten Pac-12 #2 Michigan Southern California
Cheez-It Bowl Dec. 27 Phoenix, AZ 10:15 ESPN Big 12 #5/MWC Pac-12 #6/MWC Iowa State Washington State
Cotton Bowl Dec. 28 Arlington, TX 12:00 ESPN CFP (At-large) CFP (At-large) Florida Cincinnati
Camping World Bowl Dec. 28 Orlando, FL 12:00 ABC ACC #1 Big 12 #2 Virginia Baylor
Peach Bowl Dec. 28 Atlanta, GA   ESPN CFP Semi-final CFP Semi-final Louisiana State (#1) Alabama (#4)
Fiesta Bowl Dec. 28 Glendale, AZ   ESPN CFP Semi-final CFP Semi-final Ohio State (#2) Clemson (#3)
First Responder Bowl Dec. 30 Dallas, TX 12:30 ESPN Big 12 #6 C-USA/ACC #9 Texas Chrsitian Louisiana Tech
Redbox Bowl Dec. 30 Santa Clara, CA 4:00 FOX Big Ten/MWC Pac-12 #3/MWC Iowa Washington
Music City Bowl Dec. 30 Nashville, TN 4:00 ESPN ACC #2/3/4/5/Big Ten SEC #2/3/4/5/6/7 Miami Missouri
Orange Bowl Dec. 30 Miami Gardens, FL 8:00 ESPN CFP (ACC) CFP (SEC/Big Ten/ND) Wake Forest Pennslyvania State
Belk Bowl Dec. 31 Charlotte, NC 12:00 ESPN ACC #2/3/4/5 SEC #2/3/4/5/6/7 Virginia Tech Kentucky
Sun Bowl Dec. 31 El Paso, TX 2:00 CBS ACC #2/3/4/5 Pac-12 #4 North Carolinas Arizona State
Liberty Bowl Dec. 31 Memphis, TN 3:45 ESPN Big 12 #4/AAC SEC #2/3/4/5/6/7/AAC Oklahoma State Mississippi State
Arizona Bowl Dec. 31 Tuscon, AZ 4:30 CBSS MWC #4 Sun Belt #5 Hawaii Arkansas State
Alamo Bowl Dec. 31 San Antonio, TX 7:30 ESPN Big 12 #1 Pac-12 #1 Texas Utah
Citrus Bowl Jan. 1 Orlando, FL 1:00 ABC Big Ten #1/ACC #1 SEC #1 Notre Dame Auburn
Outback Bowl Jan. 1 Tampa, FL 1:00 ESPN2 Big Ten SEC #2/3/4/5/6/7 Indiana Tennessee
Rose Bowl Jan. 1 Pasadena, CA 5:00 ESPN CFP (Big Ten) CFP (Pac-12) Minnesota Oregon
Sugar Bowl Jan. 1 New Orleans, LA 8:45 ESPN CFP (Big 12) CFP (SEC) Oklahoma Georgia
Birmingham Bowl Jan. 2 Birmingham, AL 3:00 ESPN SEC #8/ACC #10 AAC/ACC #10 Utah State? Memphis
Gator Bowl Jan. 2 Jacksonville, FL 7:00 ESPN ACC #2/3/4/5/Big Ten SEC #2/3/4/5/6/7 Wisconsin Mississippi State
Potato Bowl Jan. 3 Boise, ID 3:30 ESPN MWC #2/3 MAC Air Force Buffalo
Armed Forces Bowl Jan. 3 Fort Worth, TX 11:30 ESPN Big Ten MWC #5 Ohio Wyoming
Mobile Alabama Bowl Jan. 6 Mobile, AL 7:30 ESPN MAC Sun Belt #2 Central Michigan Louisiana-Lafayette
CFP Championship Game Jan. 13 New Orleans, LA 8:00 ESPN Peach Bowl Winner Fiesta Bowl Winner    

Teams 6-6 or better that need at-large bids: Eastern Michigan (6-6), Liberty (7-5), Fresno State (6-6)

Overall:
Scores:

?=at-large because some conference couldn't fill its bids
* = Accepted invitation
** = Predicted correctly
A team in bold indicates that I predicted the winner correctly
A team in italics means that team won the game, but was not who I picked
A bold score means that I actually managed to pick the score correctly
1: Team meets one of the exception criteria, see the blurb about bylaw 18.7.2 below.

Old predictions
Past years: 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999 | Index

Conference  Teams Eligible Teams With Bids
ACC 14 4  
Big Ten 14 7  
Big 12 10 4  
Pac-12 12 2  
SEC 14 6  
AAC 12 6  
C-USA 14 4  
MAC 12 3  
MWC 12 4  
Sun Belt 10 3  
Indepedents 6 1  
Totals 130 45  

Above table reflects all teams that are currently bowl eligible as of when this page was last updated. 78 teams are needed to fill all available bids.

The introduction of the College Football Playoff in the 2014-2015 season changed a bunch of stuff. Below is a quick guide to the process and links to sources of information.

The College Football Playoff is a new system that includes a rotating set of six bowl games (the Peach, Cotton, Rose, Fiesta, Sugar, and Orange) plus a championship game. Each year, two of the games will host semi-final games, which will be seeded according to a committee. The winners of those games will meet in the championship game. The rotation of the games is as such for the semi-finals:
2014, 2017, 2020, 2023: Rose and Sugar
2015, 2018, 2021, 2024: Orange and Cotton
2016, 2019, 2022, 2025: Fiesta and Peach

When those games aren't hosting national semi-finals, they will be the home for conference champions and other teams not selected for the semi-finals. The default matchups are:
Rose: Big Ten #1 vs. Pac-12 #1
Sugar: SEC #1 vs. Big 12 #1
Orange: Highest-ranked ACC vs. the highest-ranked available team from the SEC, Big Ten, or Notre Dame
Cotton, Fiesta, and Peach: At-large selections or the "top team" from the Group of Five (which consists of the non-autobid conferences (the American, C-USA, MAC, Mountain West, and Sun Belt). These bowls can also host the Big Ten or SEC champions if they are not in the playoff when the Rose or Sugar bowls are part of the playoff.

Other rules:
1. Notre Dame can only appear twice as an at-large
2. If the ACC faces a rematch in the Orange Bowl, then the Orange can select the highest ranked available opponent (according to the committee) and the spurned team is placed elsewhere in the framework.
3. If a conference's champion is selected for the play-off, then the next highest ranked team from that conference assumes the berth, except in the Big 12, where the conference runner-up gets it.

Future championship game sites:
2020: Miami, FL
2021: Indianapolis, IN
2022: Los Angeles, CA
2023: Houston, TX
2024: TBD
2025: TBD

"ACC #1" means "the first ACC team after the CFP selection process", not "the ACC champion".

Overall eligibility: The 2016-2017 NCAA Division I Manual (warning, PDF) bylaw 18.7.2 governs Division I FBS football eligibility. The NCAA defines a "deserving team" as a team with an equal number of wins and losses, i.e, a record of 6-6 and better against FBS opponents. For the purposes of this record, a team is also allowed to count one FCS win as well. Note that it is no longer a requirement that all above .500 teams are selected before 6-6 teams. For 2013, the NCAA added what one might call the "UCLA and Georgia Tech" rule which basically boils down to: a) winning your conference title game makes you a "deserving team" and b) losing your title game does not affect your "deserving team" status.

In addition to deserving teams, bylaw 18.7.2 also spells out what will happen if there are not enough bowl eligible teams for the 40 bowl games. Note that these criteria apply in order, and a particular bowl game may use a team from this "pool" once every four years (effective 8/2012).
1. The "counting 1 FCS win" rule only applies if the FCS team in question uses 90% of available scholarships out of 63 (so 56.7 scholarships, as FCS allows partial scholarships), so the first criteria is that any FCS school counts for the 1-win.
2. Teams that finished 6-6 with two FCS wins. This year, this rule could potentially apply to North Carolina or Army.
3. Teams that finished 6-7 (this used to be the "UCLA rule" but conference championships can no longer make a team ineligible for a bowl).
5. Teams that are reclassifying to FBS and have a 6-6 record. There are no reclassifying teams this year.
6. Teams in the top 5 of the APR and with a 5-7 record. This year, those teams are Northwestern, Air Force, Vanderbilt, Navy, and Duke.

The ACC bowl selection criteria are buried in the massive media guide (warning: huge PDF) on page 12. The ACC no longer has a "one-win rule" and instead is using a more SEC-style "general list of criteria to emphasize regionality and quality matchups". Notre Dame is eligible for all the ACC's bowls (including the Citrus), but must be within one win of the best available ACC team at the time.
The Big Ten selection process has its own page. The Citrus Bowl will pick an ACC team if the ACC faces a Big Ten team in the Orange Bowl (see below).
The Big 12 selection order.
The Pac-12 bowl selection order, on page 139.
The SEC bowl selection order. Note that of the "pool of six", the Liberty is the first off if there's not enough teams.
The American bowl lineup on page 15.
The Mountain West bowl lineup. Note that the MWC is a backup for the Cheez-It Bowl, but if used the Cheez-It Bowl gets to pick right after the Las Vegas Bowl. However, the Redbox Bowl backup slot is filled only after all the other MWC bowls are filled.
The MAC bowl lineup on page 14. This article from 2014 also talks about them a bit. The MAC is also a secondary for any ESPN owned and operated bowl games.
The Sun Belt bowl lineup on page 21.
The Conference USA bowl lineup, page 168.
As far as independents other than Notre Dame go: so far I've found statements saying BYU is eligible for "ESPN-affiliated bowls" and not much else.

Other notes:

Schedule sources: Matt Sarz, conference media guides (see above), and individual bowl websites.