Spotify just launched in the US, but if you want an account now, you either need an invite or have to start paying for the service. Fortunately, if you want to skip the queue and get a free account right now there's a pretty simple loophole.
How to Get Spotify Free Without an Invite?
You need to start with a UK account. To do that, you'll need to be in the UK—or, at least, appear to be. To do that, visit DaveProxy (or another free, UK-based proxy service) and go to spotify.com. (Note: if you're using DaveProxy, be prepared to contend with a lot of pop-up ads. Just close them as they come up. They're harmless.)
Sign up for an account on the UK site. You'll need a UK zip code, but just search for McDonald's in London and you'll find one without issue.
Once you have an account, sign out and go to spotify.com like you normally would in the US. You won't see a place to log in because that's hidden behind the signup page. Pretend you're signing up for a premium account and you'll see a message asking you already have an account and want to log in. You do, so click the associated link and log in.
Go back to spotify.com and you'll now see a black box up at the top of the site. It'll read "continue to spotify.com." Click on it.
You're in, but your account is still UK-based. You'll see your username displayed up on the top right. Click it and choose "Edit Profile."
In the "Country" menu, change "United Kingdom" to "United States" and set your zip code to whatever it actually is. Save your profile when you're done.
Download the Spotify app and log in.