While our games have not always been the closest contests (especially in Allen Fieldhouse), with Missouri gone to the SEC it is obvious that our biggest rival is gone and as such we need a new one. The proper way to determine who the new biggest rival for Kansas basketball is is probably to let one emerge organically (and in fact I think that is what has happened; more on that later) but to have some fun I will lay out three candidates and then let you, the reader, decide who our new rival will be (mainly because I need people to troll on twitter).
When Missouri left the conference I said something to the effect of "now that Missouri is gone, where are we going to find a group of fans that wears yellow and is populated largely by meth addict backwoods hicks?" and then West Virginia serendipitously appeared, saving the day.
In all sincerity, however, the Mountaineers have been one of the most underlooked (and best) programs in the country the past few years. They probably won't be very good this year (nor were they last year), but they have an average KenPom rating of 17.5 from 2006-2011, and an average rating of 22 since Bob Huggins took over (although their best two seasons under Huggins were soon after taking over for John Beilein, so perhaps the program is steadily declining under the velvet fog).
Still, other than for Missouri-like reasons, I don't see much potential for a rival in West Virginia. I don't think they'll consistently be good enough and they're too far away. It is basically a two horse race between:
The Wildcats have only beaten Kansas three times since Bill Self took over (all in Manhattan) but they are the in state rival and the games usually have an important feel to them (though, that feeling generally lasts longer in Manhattan. In Allen Fieldhouse I'm usually ready for a nap after about 5 minutes).
How much does the in state rivalry aspect overcome the "K State usually isn't very good" aspect? I'm not sure. I'm also not sure of how much I hate Kansas State. While I spent plenty of energy on hoping that Missouri would lose, I certainly rooted for K State when the two would play but beyond that never really cared about how they did one way or the other. It's certainly not to suggest that they're irrelevant (though they kind of are) just that I don't consider them much of a rival.
Of course, this all could change now that Bruce Weber is in charge in Manhattan, and no doubt Bill Self will have those two games circled on the calendar.
Still, the choice for biggest rival is, to me, an overwhelming one:
The Longhorns nabbed the #1 seed in the Big 12 tournament in 2008 and 2006, the last two times it wasn't Kansas, and also are the last team to win in Allen Fieldhouse, doing so on January 22, 2011. Other than Kansas, the Longhorns have been by far the best and most consistently good team in the league.
The games between the two are a little less important now because they have to come to Allen Fieldhouse every year thanks to double round robin play, but back when the only game was in Austin I always felt that game was for the conference title. Perhaps it says something about how dominant Bill Self has been and that maybe we don't actually have a rival that only one game every other year made me really worried, but Texas has consistently had great players and, while he is often criticized (and rightfully so a lot of the times) there is no doubt that Rick Barnes has taken that program to new heights.
Kansas faced off with Texas for the Big 12 tournament title in 2006, 07, 08 and 2011 and while Kansas won all four of the meetings, they were decided by 12, 4 (in OT), 10 and 12 points, and two of them were likely playoffs in terms of who would get a #1 seed in the NCAA tournament (one of which, 2008, seems ridiculous when looking back at how dominant that team was).
In fact, the 2007 Big 12 tournament final treated us to some of the most excellent foreshadowing of all time:
(apropos of nothing, Mario Chalmers seemed to love playing in either the Big 12 tournament or against Texas, as evidenced by his 2008 tournament final performance).
The games have always been important, they've usually been very good, they always contain elite players and future NBAers, and there is no doubt in my mind that Texas has organically morphed into our biggest rival.