"Military Intelligence" is one of those famous contradictions that is often spouted, but I am seeing more and more of late. Some examples:
Fast Food Nutritional Information
I've been working on eating better lately (and it's been fairly successful), but there is just something blindly contradictory about a fast food place having nutritional information. While not technically "fast" (or maybe even "food"), a great example can be found on the T.J. Cinnamon website. Yes, a pecan sticky bun has a total of 2026 calories (yes, that's per bun). Not to be outdone, I had to look up the calories for that Pizza Hut sandwich I had for lunch, which happened to be 640. I stripped the cheese off the bun, so I scored it at 625.
Rolling Stone's 100 Best of 00
The current incarnation of Rolling Stone has an issue out that lists the "best songs of the 00 decade". As side note/tirade, I remember when Rolling Stone was actually a larger publication that mainly covered rock/metal/alternative/pop. Now it's about 80% rap/R&B/hip-hop, etc. Anyway, I can think about 10 decent songs over the past 9 years. Maybe.
Okay, this isn't so much a contradiction by name as it is by definition. In my view, a conservative is someone who stands for self-reliance, limited government intrusion, limiting taxes and spending, etc. How then do we reconcile the notion that some conservatives want the government to intrude into the most personal aspects of our lives through things like legislating morality? It's not just being anti-gay, it's about being against virtually any personal choice that runs counter to a specific (evangelical Christian) religious code. So that individual who stands for limited government, low taxes, personal responsibility, etc. can't truly be "conservative" in some eyes because he may do something in his bedroom that others may find offensive. Score one for contradictions.