This part is the holy grail. Spotify appeals to even the cheapest of the cheap and the most persistent of bootleggers by offering its entire catalog of 15 million songs for free.
The Swedes pull this off by implementing ads in the free version: banner ads appear in the program like they would on a website, and you'll hear a 15 or 30 second radio spot after every three or four songs. The advertisements are all pretty straightforward and music related, and before long you'll hardly even notice them. All in all, it's truly a small price to pay for instant access to any album you want for free.
Spotify also has ad-less versions for a more "pure" experience-- and they're pretty cheap. For just $5 a month, you get all of Spotify's catalog with no ads at all. For $10, you get the same on your smartphone with the ability to play music even when you're offline.