One of my friends loves my use of “batshit crazy”…

…and he asked me to explain it.  So I emailed him.

Hmm.  Bat-Shit Crazy?  Typically it's a combination of all the various types of crazy you can imagine.  The craziest of the crazy.  I would assume it's a step up from "apeshit", maybe something to do with "bats in the belfry"?  I thought it may have had something to do with Bob Dylan's near-fatal episode with batshit while cave exploring, but I've found no proof.
Encyclopedia Dramatica defines it thusly:
Batshit crazy is one of the highest levels of insanity. It's usually a combination of all of the above, to wit:

Prima: Repent of your sins! Frienditto is the Antichrist! If you don't repent I will ban you from my community! Secunda: You're insane! Prima: That's defamation of character! I have unlimited disposable income and will bring you to Internet court! I will have your humility!

Urban Dictionary defines it pretty well too…

batshit crazy: adj. speech or behavior that is over the top, unhinged, self-destructive, or a threat to others.
Well, the idea and phrase comes from this political concept – there is a minority of people, around 27%, that will support whatever candidate fits their ideology regardless of any facts to the contrary.  It's also referred to as the Crazification Factor.  Here it is, explained from that previous link:
John: Hey, Bush is now at 37% approval. I feel much less like Kevin McCarthy screaming in traffic. But I wonder what his base is –

Tyrone: 27%.

John: … you said that immmediately, and with some authority.

Tyrone: Obama vs. Alan Keyes. Keyes was from out of state, so you can eliminate any established political base; both candidates were black, so you can factor out racism; and Keyes was plainly, obviously, completely crazy. Batshit crazy. Head-trauma crazy. But 27% of the population of Illinois voted for him. They put party identification, personal prejudice, whatever ahead of rational judgement. Hell, even like 5% of Democrats voted for him. That's crazy behaviour. I think you have to assume a 27% Crazification Factor in any population.

John: Objectively crazy or crazy vis-a-vis my own inertial reference frame for rational behaviour? I mean, are you creating the Theory of Special Crazification or General Crazification?

Tyrone: Hadn't thought about it. Let's split the difference. Half just have worldviews which lead them to disagree with what you consider rationality even though they arrive at their positions through rational means, and the other half are the core of the Crazification — either genuinely crazy; or so woefully misinformed about how the world works, the bases for their decision making is so flawed they may as well be crazy.

John: You realize this leads to there being over 30 million crazy people in the US?

Tyrone: Does that seem wrong?

John: … a bit low, actually.

As far as examples, I think Michael Jackson, Whitney Houston, Ann Coulter, Mel Gibson, and Tom Cruise work nicely as examples.  Someone's spouse might fit the bill, someone's mom who fancies whales and traps cats might qualify as well.  And I'm pretty sure that the people who have 75 cats living in one house might be batshit insane too.