Robespierre speaks the truth.
I've done hundreds, perhaps thousands of emails including my credit card informtion and never had the information abused or stolen.
Yet recently we went through some identity theft problems with my partner's card -- which has never been used on the internet. We strongly suspect it was from a restaurant, just as Robespierre suggests.

<faxing information is the least secure method of sending information>

Please explain if you are such an expert.

Although most hotels I've used don't actually run through my CC number until we settle the bill, the whole point of giving the hotel the CC number in the first place is so they can charge you the penalty for late cancellation or no-show. Since it is becoming more common for CC companies to require parties provide proof of legitimate CC number use, the hotel's request is probably legit. If you're going to trust them with your CC number (and presumably you've researched the hotel) you might as well be hung for a sheep as a lamb, as they say, and give them the code. It's the 3-digit thing on the back of the card.

If you're worried about sending stuff by email over an unsecured server (i.e. no little padlock symbol appears in the lower right hand portion of your screen), split up your credit card number and send the two parts in two separate emails. I've done this lots of times. It's probably overkill, but it's no big deal to do it, either. Nor have I ever had a hotel object to this practice.

My only hope is that merchants take care where they write down/record the security code. If it should become as accessible as a credit card number, the whole point of the code is lost.

I'll handle that one. I think the reference was to the fact that often when you fax such information it will lie on a machine for hours or even a day or so open to anyone who might pass by it. I've walked by fax machines by hotel desks and seen received faxes sitting there that if I wanted to, I could have easily picked up. Certainly any employee of a hotel, as well as total strangers then have access to that information -- including cleaning people if they come in overnight.

Ooops. Sue snuck her response in on me there. My comment above was in reference to ThinGorjus' comment.