I've been a happy user of emusic.com for over a year now. Basically their business model is selling subscriptions that entitle the user to download a certain amount of no-strings-attached non-drm mp3s per month (starting from 40 songs/month for $9.99). Originally I signed up just to get the 50 free downloads that they offer for new subscribers, found enough interesting stuff to continue with the cheapest subscription, and finally had to upgrade to 65 songs/month (for $14.99/month) since my "save for later" list was starting to get too long.
A few reasons I like emusic:
The price per song is hard to beat, about 80-90% cheaper than the approximate price per song on CDs bought in Finland.
They have a pretty good selection of the sort of music that I like, and some of it is stuff that would be hard to find in record stores around here. Your mileage may vary.
There are reasonable tools for finding new music that I might like.
The music isn't copy protected in any way, so I can be reasonably sure that no matter what I do I won't be breaking the new Finnish copyright law (passed by the corrupt politicians a few months ago).
It's by no means a perfect service, but definitely worth a try.