It depends what you want to order. I know you said CDs -- I wanted to buy a video game from there and it told me that certain items, including video games, can only be delivered to select european countries (it went on to list them.) I don't remember if CDs were on that restricted shipping list....
I've ordered CDs from Amazon UK. European bands usually release stuff over their MONTHS before their CDs are available in the US. The shipping is a little slow (2 or 3 weeks), and a bit more expensive, but if it is something you can't find here, I think it is a good way to go.
I've never ordered from them, but smokecds.com is an awesome Australian site that I've ordered from. I think shipping was about 7-10 days. And w/ the exchange rate things are real cheap.
Yup, I can't find the CD's I want on the US site, so it's going to have to be the UK version if I want them. Unfortunately, my music tastes don't allow me to buy a lot from the US (I'm a huge electronica girl-specifically Happy Hardcore)
I figured it would cost me about $70 for the 3 CD's I want (each one is a double-disc set), including shipping, so it's not totally horrible.
I've ordered CDs from Amazon UK since 2003 and have never had any problems. I too don't have very American music taste so I understand your dilemma. Specifically, I get the NOW UK compilations. The shipping isn't super fast (it may be due to the fact that I'm on the west coast), but it gets. Also, don't be alarmed if there's no plastic wrapping. BF found out on a UK music forum that they don't shrink-wrap CDs there apparently.