Mobile version. Acronyms are explained below. All times Eastern and PM, except where obvious. As of 11/18/2018 07:55:11 PM -0800.

Bowls When Where Time TV Teams Predictions
New Mexico Bowl Dec. 15 Albuquerque, NM 2:00 ESPN MWC #2/3/4 C-USA Utah State Alabama-Birmingham
Cure Bowl Dec. 15 Orlando, FL 2:30 CBSS AAC #7 Sun Belt #4 Tulane Louisiana-Lafayette
Las Vegas Bowl Dec. 15 Las Vegas, NV 3:30 ABC Pac-12 #5 MWC #1 Arizona State Fresno State
Camellia Bowl Dec. 15 Montgomery, AL 5:30 ESPN MAC #1/2/3/4/5 Sun Belt #3 Eastern Michigan Appalachian State
New Orleans Bowl Dec. 15 New Orleans, LA 9:00 ESPN C-USA Sun Belt #1 Louisiana Tech Troy
Boca Raton Bowl Dec. 18 Boca Raton, FL 7:00 ESPN AAC #1/2/3/4/5/6/MAC C-USA/MAC South Florida Florida International
Frisco Bowl Dec. 19 Frisco, TX 8:00  ESPN AAC #1/2/3/4/5/6/C-USA MAC #1/2/3/4/5/C-USA Southern Methodist Buffalo
Gasparilla Bowl Dec. 20 Tampa, FL 8:00 ESPN ACC #9/C-USA AAC #1/2/3/4/5/6 Florida Atlantic? Cincinnati
Bahamas Bowl Dec. 21 Nassau, Bahamas 12:30 ESPN MAC #1/2/3/4/5 C-USA Northern Illinois Middle Tennessee State
Potato Bowl Dec. 21 Boise, ID 4:00 ESPN MWC #2/3/4 MAC #1/2/3/4/5 Boise State Toledo
Birmingham Bowl Dec. 22 Birmingham, AL 12:00 ESPN SEC #8/ACC #10 AAC #1/2/3/4/5/6/ACC #10 Brigham Young? Memphis
Armed Forces Bowl Dec. 22 Fort Worth, TX 3:30 ESPN AAC #1/2/3/4/5/6 Big 12 #6 Houston Army?
Dollar General Bowl Dec. 22 Mobile, AL 7:00 ESPN MAC #1/2/3/4/5 Sun Belt #2 Ohio Georgia Southern
Hawaii Bowl Dec. 22 Honolulu, HI 10:30 ESPN MWC #2/3/4 C-USA Hawaii Marshall
First Responder Bowl Dec. 26 Dallas, TX 1:30 ESPN Big Ten C-USA/ACC #9 Wyoming? North Texas
Quick Lane Bowl Dec. 26 Detroit, MI 5:15 ESPN Big Ten/MAC ACC #8/MAC Miami? Miami
Cheez-It Bowl Dec. 26 Phoenix, AZ 9:00 ESPN Big 12 #5/MWC Pac-12 #6/MWC Texas Tech California
Independence Bowl Dec. 27 Shreveport, LA 1:30 ESPN ACC #7/AAC/C-USA SEC #9/AAC/C-USA Duke Southern Mississippi?
Pinstripe Bowl Dec. 27 New York, NY 5:15 ESPN ACC #2/3/4/5 Big Ten Syracuse Purdue
Texas Bowl Dec. 27 Houston, TX 9:00 ESPN Big 12 #3 SEC #2/3/4/5/6/7 Iowa State Mississippi State
Music City Bowl Dec. 28 Nashville, TN 1:30 ESPN ACC #2/3/4/5/Big Ten SEC #2/3/4/5/6/7 Boston College Vanderbilt
Camping World Bowl Dec. 28 Orlando, FL 5:15 ESPN ACC #1 Big 12 #2 North Carolina State West Virginia
Alamo Bowl Dec. 28 San Antonio, TX 9:00 ESPN Big 12 #1 Pac-12 #1 Texas Washington
Peach Bowl Dec. 29 Atlanta, GA 12:00 ESPN CFP (At-large) CFP (At-large) Georgia Pennslyvania State
Belk Bowl Dec. 29 Charlotte, NC 12:00 ABC ACC #2/3/4/5 SEC #2/3/4/5/6/7 Pittsburgh South Carolina
Arizona Bowl Dec. 29 Tuscon, AZ 1:00 CBSS MWC #5 Sun Belt #5 San Diego State Arkansas State
Cotton Bowl Dec. 29 Arlington, TX 4 or 8 ESPN CFP Semi-final CFP Semi-final Alabama (#1) Michigan (#4)
Orange Bowl Dec. 29 Miami Gardens, FL 4 or 8 ESPN CFP Semi-final CFP Semi-final Clemson (#2) Notre Dame (#3)
Military Bowl Dec. 31 Annapolis, MD 12:00 ESPN ACC #6 AAC #1/2/3/4/5/6 Virginia Temple
Sun Bowl Dec. 31 El Paso, TX 2:00 CBS ACC #2/3/4/5 Pac-12 #4 Georgia Tech Oregon
Redbox Bowl Dec. 31 Santa Clara, CA 3:00 FOX Big Ten/MWC Pac-12 #3/MWC Nevada? Stanford
Liberty Bowl Dec. 31 Memphis, TN 3:45 ESPN Big 12 #4/AAC SEC #2/3/4/5/6/7/AAC Oklahoma State Missouri
Holiday Bowl Dec. 31 San Diego, CA 7:00 FS1 Big Ten Pac-12 #2 Iowa Utah
Gator Bowl Dec. 31 Jacksonville, FL 7:30 ESPN ACC #2/3/4/5/Big Ten SEC #2/3/4/5/6/7 Wisconsin Auburn
Outback Bowl Jan. 1 Tampa, FL Noon ESPN2 Big Ten SEC #2/3/4/5/6/7 Michigan State Texas A&M
Citrus Bowl Jan. 1 Orlando, FL 1:00 ABC Big Ten #1 SEC #1 Northwestern Kentucky
Fiesta Bowl Jan. 1 Glendale, AZ 1:00 ESPN CFP (At-large) CFP (At-large) Florida Central Florida
Rose Bowl Jan. 1 Pasadena, CA 5:00 ESPN CFP (Big Ten) CFP (Pac-12) Ohio State Washington State
Sugar Bowl Jan. 1 New Orleans, LA 8:45 ESPN CFP (Big 12) CFP (SEC) Oklahoma Louisiana State
CFP Championship Game Jan. 8 Santa Clara, CA 8:00 ESPN Rose Bowl Winner Sugar Bowl Winner    

Teams 6-6 or better that need at-large bids: Coastal Carolina (6-6), Louisiana-Monroe (6-6), Western Michigan (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: 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 9  
Big Ten 14 7  
Big 12 10 5  
Pac-12 12 7  
SEC 14 10  
AAC 12 6  
C-USA 14 6  
MAC 12 6  
MWC 12 6  
Sun Belt 10 6  
Indepedents 6 3  
Totals 130 71  

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 Chick-fil-A, 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:
2014-2015, 2017-2018: Rose and Sugar Bowls
2015-2016, 2018-2019: Orange and Cotton Bowls
2016-2017, 2019-2020: Fiesta and Chick-fil-a Bowls
This will continue through the 2025-2026 season.

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.

"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 10. 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). See also the Big Ten bowl tracking page.
The Big 12 selection order.
The Pac-12 bowl selection order, on page 3.
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 14.
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. 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's weekly press releases list their tie-ins in selection order, which is very nice of them.
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: CollegeFootballPoll, Matt Sarz, conference media guides (see above), and individual bowl websites.