While the B1G Hockey Conference is only in its second year, 5 of the 6 teams have been playing for over 50 years. Michigan, Michigan State, and Minnesota were founding members of the WCHA (Western Collegiate Hockey Association) and have been playing each other for many years. Wisconsin joined the WCHA in the 69-70 season. Michigan and Michigan State left for the CCHA (Central Collegiate Hockey Association) in 81-82. Ohio State was a founding member of the CCHA in 1971-72.
For the most part, only Michigan, Michigan State, Minnesota, and Wisconsin have well established rivalries as Penn State is too new and Ohio State is a sub-.500 program.
Everyone hates North Dakota. The hatred for North Dakota is analogous to the hatred for Notre Dame in football. North Dakota's greatest benefactor, Ralph Englestad, was an alleged Nazi sympathizer who had a large collection of Nazi memorabilia.
This is the primary rivalry for both teams. These teams have faced off 302 times with Michigan leading the series 153-129-19. These teams regularly face off in the Great Lakes invitational for non-conference games (as they did this season). Starting in the 90-91 season, these teams have faced off at Joe Louis Arena in the Rivalry at the Joe Series. The first two years saw each team "host" a game at The Joe. Starting in 1993, only one game has been played at The Joe. MSU hosts in odd years while UM hosts in even years. Michigan leads the Rivalry at the Joe Series 14-10-4. These two kicked off the outdoor hockey craze in 2001 with the Cold War in East Lansing.
These teams are the two winningest programs in College Hockey. Minnesota has 1683 wins (.629 w%) to Michigan's 1592 (.605 w%). Minnesota leads the series 132-121-15. These teams have played for the Mariucci-Renfrew Trophy since 1993 with Minnesota winning it 10 of 19 times. The trophy is named for legendary coaches John Mariucci (MN) and Al Renfrew (UM). The winner of the season series wins the trophy. Since the teams split this season, I believe the Minnesota will keep it. If they meet in the BTT or the NCAA tourney this may change but I'm not sure.
Like Michigan, Michigan State also plays Minnesota for a trophy. The winner of the season series wins the Mariucci-Bessone Trophy. Minnesota leads the series, which also began in 1993, 11-5-5. Minnesota leads the overall series 105-43-14.
Depending on who you talk to this is either number 1 or 1a for Minnesota fans and number 1 for Wisconsin fans. The Gophers lead the series 160-91-22. These teams and their fans do not like each other.
This is not The Game, but these schools and their fans never like facing each other. Michigan leads the series 75-33-12.
Former Conference Rivals
Minnesota leads the series 146-130-15. This is my most hated rival and many other Gopher fans would agree. Minnesota, Michigan, and Michigan State left the WCHA for the 58-59 season due to shady recruiting practices by a few of the other WCHA schools including NoDak. In their most recent meeting, Minnesota defeated North Dakota in last year's Frozen Four on a Justin Holl goal with 0.6 seconds left in the third. There is a lot of animosity between the teams and fans.
Wisconsin leads the series 86-64-11. This is another bitter rivalry with little love between teams and fans.
Michigan and MSU - Other Michigan Schools
Michigan Tech, Nothern Michigan, Ferris State, Lake Superior State, and Western Michigan (and formerly Wayne State) all sport D-1 teams which view Michigan and MSU as rivals. These teams will face off in the Great Lakes Invitational.
While this rivalry has cooled off in recent years, it was really prominent from 1963-1995. These teams famously had a bench clearing brawl in the 1976 NCAA semifinal which Minnesota won 402 en-route to a National Championship. Minnesota and BU have split the series 12-12-2. This is the only active team that Minnesota does not have a winning record against.
Minnesota - Other Minnesota Schools
Minnesota-Duluth, Saint Cloud State, Minnesota State-Mankato, and Bemidji State all sport D-1 programs that view Minnesota as a rival. These teams all face off in the North Star College cup post B1G re-alignment.
Not a real rivalry, but this is the only team that Minnesota has a losing record against (0-4-0). Maybe ASU getting a D1 program will convince some PAC12 schools to join D-1 so Minnesota can correct this.
Former WCHA Rivals
Minnesota and Wisconsin (and to a lesser extent Michigan and MSU) also see former WCHA foes as rivals. These teams include Colorado College, Denver University, St. Cloud, and Duluth.
Former CCHA Rivals
Michigan, MSU, and, to a lesser exetent, OSU also see Miami (OH) and Notre Dame as lesser rivals as these were teams challenging for the CCHA Crown. OSU fans, did you see Bowling Green as a rival in hockey?