The Nebraska Cornhuskers have a few notable rivalries, and which one is considered the «biggest» can vary depending on who you ask and the era of college football you’re referencing. However, here are a couple of the most prominent:
Oklahoma Sooners:
Historically, this has been a major rivalry. Especially during their time together in the Big Eight and Big 12 conferences, the Nebraska-Oklahoma games were often highly anticipated and intensely competitive.
Colorado Buffaloes:
The Colorado-Nebraska rivalry has also been very significant.1 There have been periods of intense competition between these two teams, and the rivalry has seen a resurgence in recent years.2
Iowa Hawkeyes:
Now that Nebraska is in the Big Ten conference, Iowa has become a major rival. Due to the proximity of the two states, and the fact that they play each other yearly, this rivalry has grown in recent years.
Therefore, while there are a few teams that could be named, historically Oklahoma is very high on that list, and currently Iowa and Colorado are also very large rivals.