Well, here's a new dilemma for me.
I've been asked to send 60 euros (!) as a deposit for a reservation in Croatia. I have the name and bank address only. Is Western Union the way to go? I am completely clueless, have never done this before in 40 years of travelling.

For euro payments...

Paypal and Moneybookers are internet services I've used.

I've also sent cash (registered), bank wire transfer, bank draft, and Western Union. Lastly, VISA.

The wire and Western Union are the most expensive.

Cash or bank draft would the way I'd go.

I was also asked to used Western Union for a deposit in Croatia a couple of years ago. It seems common over there, as many accommodation owners are not set up for other forms of payment. It was easy enough to do, just Google for Western Union and follow the instructions on the web site. They did phone me up to ensure that I was aware of the risk of fraud - i.e. you are wiring cash to someone you don't know - but as the sum involved isn't huge, I carried on and all was fine. The owner mailed me to say when she has received the deposit and I payed the balance in cash when I arrived.

Money transfers for relatively small amounts of money can be unduly expensive - I have even resorted to paying a small deposit in euros by posting the cash, registered mail! For 40 euros it was not worth the expense of a bank transfer and it arrived safely.

Thanks for the help, people. I am still dithering: as you say the charges are out of all proportion to the amount of money sent. I have both UK and US bank accounts and the UK one seems more familiar with this kind of thing. But what a hassle. Am seriously thinking of sending cash by registered mail.

Using WU has to do with their ability to get hard cash in some places. Look into the money gram that WU has.

How much does it cost to send a bank draft? Would that work? For me, I can get it done for $5, plus 1% over the interbank rate.

WillTravel: how do I go about sending a bank draft? Through Western Union? Or through my bank in US? Do I send it to a person at an address or to a bank?

You would send the bank draft, which looks similar to a check, to the person's postal address. It will be in the desired currency, and then the person deposits it in their bank just like any other check.

A bank can help you obtain a bank draft. I have obtained a bank draft from a currency exchange provider.