Rivalry time: Nobody
Rutgers never had and doesn't have a staunch rivalry with anybody. This is likely due to them being independent forever. However, it looks like the Big Ten, Maryland, and Penn State are going to just force some rivalries so that the newcomers don't feel left out. I'm all for a heated rivalry, but they don't grow on trees. You can't just make a trophy and say, "Hey, let's battle over this piece of plastic." In the article, Delaney says that he thinks "these rivalries will happen quite naturally based on a bad officiating call, a great individual performance, an upset, securing a championship." But the fact that these schools are already "looking" to create a rivalry lessens the importance of said rivalry once, or if, it happens "organically." Rivalries aren't built in a year or two because one team pissed off another team or someone got screwed over by a bad call or someone pulled a huge upset. If that were the case, Michigan would be hosting a rival on August 30th this season rather than a non-conference opponent that shocked us a handful of years ago. Don't get me wrong, I hope Rutgers ends up succeeding and building rivalries with Big Ten schools. Since they are a part of the conference for the foreseeable future, they might as well become acclimated. But forcing something as deep-rooted as a rivalry seems silly. Let's wait half of a decade and see what happens. Then we can start talking about building trophies for Rutgers (and Maryland).
The Birthplace of College Football: Nov. 6, 1869 vs. Princeton University
In what's considered the first intercollegiate football game, Rutgers College defeated the College of New Jersey (now known as Princeton University) by a score of 6-4. They were the only two teams in existence at the time and played one more contest that year, in Princeton, which the Tigers won 8-0. Due to both squads holding 1-1 records, they've both been considered National Champions (retroactively, of course) for the 1869 season.
However, it should be noted that the games played by Rutgers and Princeton in 1869 did not resemble today's rendition of football, but more closely mirrored rugby and soccer. I suggest reading a full summary of the game, but below is a brief description:
"Each score counted as a "game" and 10 games completed the contest. Following each score, the teams changed direction. The ball could be advanced only by kicking or batting it with the feet, hands, heads or sides."
This was before touchdowns, the forward pass, and a standard rule book. For instance, the home team for each game enforced a slightly different set of rules: Princeton awarded a free kick for any ball caught clean and on the run, which helped them avenge their loss. However, archaic rules aside, these two teams set the stage for college football, and the importance of their game can't be overstated.
Two undefeated seasons: 1961 at 9-0 and 1976 at 11-0
Even though they're one of the oldest teams in college football history, the Scarlet Knights haven't enjoyed much success through the years. Their one claimed National Championship came over 140 years ago, they made one bowl appearance prior to 2005, and they only have two seasons with double-digit wins: 11-2 in 2006 and the undefeated 1976 season. They've only won four conference titles (three Middle Atlantic and one Big East); however, that total is skewed by the fact that Rutgers was independent for the vast majority of its existence until joining the Big East in 1991. For instance, those three Mid Atlantic conference championships occurred during the four years they were actually in it.
When they went undefeated in 1961, Rutgers won the Middle Atlantic in their final season in the conference. Along with Alabama, they were the only undefeated team at year's end and finished ranked #15 in the AP. In 1976, Rutgers was once again independent and finished ranked #17 in the AP. The reason why the Scarlet Knights didn't crack the top ten (or make a case for a National Championship) in either of their undefeated seasons was because of their schedule. In both season, Rutgers played a combination of independent, mid-major, or Ivy League schools. In other words, not the strongest schedules in the world. Take '76 for example. Only two teams that Rutgers defeated finished the year with a winning record: Lehigh (mid-major) at 6-5 and Colgate (independent) at 8-2.
After a couple of decades in the Big East and now transitioning to the Big Ten, Rutgers won't have to worry about strength of schedule moving forward, and a third undefeated season would earn more than a ranking in the mid-teens.
So that's about it for Rutgers football. Even though they've been around forever, they don't have much to show for it.