Question: Which Boston radio station broadcasts the Red Sox games?

Boston Red Sox Radio Network

The Boston Red Sox Radio Network consists of 61 stations (39 A.M., 22 F.M. and 7 F.M. translators) in the 6 New England states, along with New Mexico, New York, and Wyoming.[1]  The primary English-language announcers are Joe Castiglione and Tim Neverett, who alternate play-by-play and color commentary.[2] In 2015, Rob Bradford and Lou Merloni  filled in for former announcer Dave O'Brien when he called Monday Night Baseball for ESPN.[3] Mike Mutnansky serves as pre- and post-game host.
In addition to the English-language network, there is a 2-station Spanish-language network (both A.M.) with affiliates in italics.  This brings the total number of stations carrying Red Sox baseball to 63.  The "Red Sox Radio Network" specifically refers to the English-language network originating at WEEI-FM.  The Spanish-language network, with Uri Berenguer announcing, is called the "Spanish Beisbol Network".
Shaw's and Star Market Supermarkets, a grocery store chain which serves much of New England, is the primary promotional sponsor of Red Sox' English-language radio broadcasts.  Thus, the announcers refer to the "Shaw's and Star Market WEEI Red Sox Radio Network" when entering into commercial spot breaks during the broadcast.
List of radio network stations

Flagships (2 stations)
1490/WCCM: Haverhill, Massachusetts (Spanish)
93.7/WEEI-FM: Lawrence, Massachusetts (Boston) (flagship)
Affiliates (60 stations + 6 translators)
Connecticut (5 stations)
800/WLAD: Danbury
1490/WGCH: Greenwich
1080/WTIC: Hartford clear-channel station
1350/WINY: Putnam (AM stereo)
1400/WILI: Willimantic
Maine (11 stations)
92.9/WEZQ: Bangor[4]
92.7/WQDY-FM: Calais
1370/WDEA: Ellsworth
99.3/WKTJ-FM: Farmington
96.3/WJJB-FM: Gray
100.1/WHOU: Houlton
105.5/WBYA: Islesboro
95.3/WALZ: Machias
1440/WRED: Westbrook
Massachusetts (13 stations + 2 translators)
96.3/WEII: Dennis
105.5/WWEI: Easthampton (Springfield)
1480/WSAR: Fall River
1400/WHTB: Fall River (if there is a conflict on WSAR)
1280/WPKZ: Fitchburg (1967-2011, 2013-2017)
105.3/W287BT: Fitchburg (relays WPKZ)
104.9/WBOQ: Gloucester (2006-2017)
860/WSBS: Great Barrington
94.1/W231AK: Great Barrington (relays WSBS)
1490/WMRC: Milford
1420/WBSM: New Bedford
1230/WNAW: North Adams
1420/WBEC: Pittsfield
830/WCRN: Worcester (2007-2009, 2011-2017)
1440/WVEI: Worcester
New Hampshire (11 stations + 2 F.M. translators)
1240/WFTN: Franklin
1270/WTSN: Dover
98.1/W251CF: Dover
1400/WTSL: Hanover
107.7/WTPL: Hillsborough
1290/WKBK: Keene
1490/WEMJ: Laconia
107.3/W297BS: Laconia
1250/WGAM: Manchester
900/WGHM: Nashua
99.7/WNTK-FM: New London
1300/WPNH: Plymouth
New Mexico

New York (4 stations + 1 F.M. translator)
1590/WRSB: Brockport (Rochester market simulcast with WOKR as "The Team") [5]
1310/WOKR: Canandaigua (Serving the Rochester market as "The Team" simulcast with WRSB)
101.3/WCPV: Essex (Serving the Burlington, Vermont/Plattsburgh, New York market)
105.1/W286AE: Fairport (rebroadcasts WOKR)
980/WOFX: Troy (Albany) (2012-2014)[6]
Rhode Island (2 stations)
103.7/WVEI-FM: Westerly
1240/WOON: Woonsocket (if there is a conflict on WVEI-FM)
Vermont (11 stations + 3 translators)
96.5/W243AT Barre (relays WDEV-FM)
1370/WBTN: Bennington
1490/WINQ: Brattleboro
101.9/W270BR Island Pond (relays WDEV-FM)
93.9/WLVB: Morrisville
1490/WIKE: Newport (A.M. stereo)
1320/WCVR: Randolph
1380/WSYB: Rutland
1340/WSTJ: St. Johnsbury
1480/WCFR: Springfield (Listed as a New London, N.H. affiliate)
106.5/W293BH: Springfield  (relays WCFR)
96.1/WDEV-FM: Warren
550/WDEV: Waterbury
93.9/WWOD: Woodstock
Wyoming

Former flagships (6 stations)
680/WRKO: Boston (1989-1994, (with WROR, 1989–90); 2007-August 25, 2009 (co-flagship with WEEI))
850/WHDH: Boston (1946-1975)
850/WEEI: Boston (1995-2012; weekday afternoon and occasional night games only from 2007-August 2009)
950/WROL: Boston (Spanish)
1390/WPLM: Plymouth, Massachusetts (1983–89)[7]
1510/WMEX/WITS: Boston (1975-1982)[8]
99.1/WPLM-FM: Plymouth, Massachusetts (1983–89)[7]
Former affiliates (66 stations)
560/WCKL: Hudson, New York
560/WHYN: Springfield, Massachusetts (through 2006)
580/WTAG: Worcester, Massachusetts (circa 1967-2006)
610 WGIR: Manchester, N.H. (1997)
620/WZON: Bangor, Maine (1994–2017)[4]
630/WPRO: Providence, R.I. (1986-2005)
730/WJTO: Bath, Me. (1997)
930/CFBC: Saint John, New Brunswick (1997)
930/WIZR: Johnstown, New York (-2012) (was an affiliate in 1997)
940/WGFP: Webster, Massachusetts (2005)
940/WINE: Danbury (1997)
960/WSVU: North Palm Beach, Florida (20??-2012)
970/WESO: Southbridge, Massachusetts (1997)
990/WALE: Greenville, R.I. (2005, 2008)
990/WCMF: Rochester, N.Y. (1997)
1010/WCNL: Newport, New Hampshire (????-2012)
1110/WHIM: East Providence, R.I. (unknown date)
1110/WCCM (now WMVX): Salem
1120/WPRX: Bristol, Connecticut (2005)
1160/WSKW: Skowhegan, Maine (????-2005)
1200/WTLA: Syracuse, N.Y. (2010–2011)
1220/WQUN: Hamden, Connecticut (????-2012)
1220/WRIB: Providence, R.I.
1230/WERI: Westerly, R.I. (1997)
1230/WJOY: Burlington, Vermont (????-2012)
1230/WMOU: Berlin, New Hampshire (????-2012)
1230/WNEB: Worcester
1240/WHMQ: Greenfield, Massachusetts (-2012)
1240/WSYY: Millinocket, Maine
1270/WTSN: Dover, New Hampshire (1997)
1280/WFAU: Gardiner, Maine (????-2012)
1350/WNLK: Norwalk, Connecticut (1997)
1380/WNRI: Woonsocket, R.I. (1997)
1390/WEGP: Presque Isle, Maine
1400 WVAE: Biddeford, Maine (????-2006)
1400/WHMP: Northampton, Massachusetts (????-2012)
1400/WLTN: Littleton, New Hampshire (????-2012)
1400/WSTC: Stamford, Connecticut (1997)
1420/WASR: Wolfeboro, New Hampshire (????-2012)
1420/WRSA: St. Albans, Vermont (-2012)
1440/WRED: Westbrook, Maine (????-2012)
1440/WSGO: Oswego, N.Y. (2010–2011)
1450/WKXL: Concord, New Hampshire (1997)
1450/WKRI: West Warwick, R.I. (1997)
1450/WTSA: Brattleboro, Vermont (late 1960s-early 1970s?)
1470/WSRO: Marlborough, Massachusetts (1997)
1490/WFAD: Middlebury, Vermont (????-2012)
1490/WUVR: Lebanon, New Hampshire (????-2012)
1570/WPEP: Taunton, Massachusetts (2004-2005)
1600/WHNP: East Longmeadow, Massachusetts (????-2012)
92.7/WEZR-FM: Norway, Maine (1997)
93.5/WCFR-FM: Springfield, Vermont (1997)
94.9/WSYY-FM: Millinocket, Me. (1997-2015)
95.1/WXTK: West Yarmouth, Massachusetts (-2012)
95.5/WBRU: Providence, R.I. (2008 overflow)
96.7 WCME: Boothbay Harbor, Maine (Until 2006)
96.7/WQSO: Rochester, New Hampshire (????-2015)
98.3 WHAI-FM: Greenfield, Massachusetts
100.1/WPNH-FM: Plymouth, N.H. (1997)
100.7/WOXO-FM: Mexico, Maine (1997)
101.1/WWKJ (now WFRQ): Mashpee, Massachusetts (1998)
101.7/WOZI: Presque Isle, Me. (1997)
101.9/WCIB: Falmouth, Massachusetts (overflow station for WXTK until 2012)
102.5/WQSS: Camden, Maine (1990s-Early 2000s)
103.1/WZON-FM: Dover-Foxcroft, Maine (????-2011)
104.7/WQEZ: Kennebunkport, Maine (1997)
104.9/WSRD: Altamont, New York
105.5/WAXB: Paterson, New York (1997)
[9]
See also
List of XM Satellite Radio channels
List of Sirius Satellite Radio stations
List of Boston Red Sox broadcasters