We don't have a real "rivalry" because NW has been just terrible in both sports for most of the modern era. Then Barnett happened in football, but the rivalry never really developed because when they were good, we were bad and vice versa. So there really has never been any meaningful game played between the two schools with anything at stake.
For hoops OTOH, we had a really intense rivalry with Iowa, Indiana and Michigan in the 80s. Michigan was always hated by everyone in the B1G and we hated them more because of Bo Schembechler and his efforts to get us in trouble with the conference and NCAA in the early 80s. Indiana was a rival because of the feuding between Henson and Knight, who many suspected of being involved in the NCAA witch hunt in the late 80s. I'd hope that I don't have to mention why Iowa was included.
Those were great times because (IMO) the 80s thorough the mid 90s were the absolute pinnacle of college hoops. There were some early entrants to the NBA, but many of the top players stayed at least 3 years, so the talent playing was really, really good. Since then it's dropped way off with so many kids leaving after a year.
We also have always had a good rivalry with Purdue because we're close geographically and have always been battling with them for the lead in Big Ten wins, titles and they are one of the few B1G programs we have a losing record against.
More recently we had a solid rivalry with MSU and Wisconsin because that 3some was the best of the league in the early 2000s. They've both been able to remain up there while of course we've dropped back.
The rest of the conference doesn't really measure up as rivals, IMO. For some reason Ohio St doesn't seem to have ever been much of a rivalry in hoops. Historically we've dominated the series by a surprising margin. More recently, they've dominated us, but it seems to me their fans just don't have much passion for hoops and that impacts any feelings of rivalry there.