Just to be clear, the Wisconsin Badgers are not "without rival." The team lost six games last year and has now lost three straight bowl games (granted these games were of the Rose Bowl variety). There are clearly teams that are on par with and surpass the Badgers. What Wisconsin does lack though, is "a rival."
The Badgers traditional rival is the Minnesota Golden Gophers. The Big Ten protects this game as Wisconsin's rivalry game, but the Badgers have prevailed in 16 of the team's last 18 meetings. A rivalry needs to be competitive, and while Jerry Kill is a great coach, the Gophers are still a few years away from being able to challenge Wisconsin. Paul Bunyan's Axe remains one of the best trophies in college football, but it has become a Madison fixture instead of a coveted spoil of victory.
Wisconsin and Michigan St. had a pretty heated recent history, however Big Ten scheduling means these two teams will not be playing each other for a couple of years. It is possible that the rivalry continues in the Big Ten Championship Game, but with Michigan St. taking a step backwards last year, the resurgence of Michigan, and the end of Ohio St.'s bowl ban, this seems unlikely.
Ohio St. could emerge as Bucky's best rival. Ohio St. plays in the same division as Wisconsin and the two are considered to be among the elite of the Big Ten. For a rivalry to thrive however it needs fan passion, and Buckeye fans will always be more interested in hating Michigan than goes on in Madison.
Maybe it is time to see if Wisconsin can manufacture a rivalry. The Badgers could reach out to strength of schedule starved Boise St. (or even Florida St.) to see if they were interested in a long term scheduling agreement. Also, Barry Alvarez and Bret Bielema could prove no love was lost between the two and schedule 10 years of home-and-home Bielema Bowls. A thought that is as tantalizing as it is unlikely.
While the lack of a rivalry game is not the end of the world for the Badgers, it is something that they should at least try to remedy. Rivalry games get programs national attention and coveted television time slots. The Badgers should try to get creative and acquire a rival or at the very least pray that the Jerry Kill turnaround in Minnesota happens sooner rather than latter.