This is one of my favorite mics from my collection, the beyerdynamic M-380:
It probably shouldn't be my favorite. I rarely use it. It has proximity effect for days, so it can be somewhat unforgiving of careless placement. It is bidirectional, which can make it difficult to use (e.g. you have to account for what the back side is going to hear, unlike with a Cardioid mic). The element is fragile, and if it breaks it cannot be repaired (because the headphone driver inside the mic went out of production 20+ years ago).
So, it's fairly irrational for me to have such a soft spot for this mic. But it was one of the first I ever acquired, a gift from my parents. It has sentimental value. It's probably collectible. It is a well-respected mic on bass cab and kick drum, and the last time I brought it to a guitar session the engineer was flipping out about it (even though he would have paired it with a '57). It feels like a secret weapon, lurking in my mic locker, waiting to be unleashed.
What's your irrationally favorite mic?