Update 2016: I wrote this piece when Spotify had just launched in the US. They've since added a My Library view. Looking back on it, it's such an obvious feature. I wonder how many people it was immediately clear to that they'd have to get around to it eventually.
I've been using Spotify for a whole two days now since it launched in the US. I'll probably write more later, but for now I'm compelled to point out a glaringly obvious missing feature in its iPhone app. I recently posed this idea on Spotify's official forum on the customer service portal, Get Satisfaction:
Add "Library" view to iPhone app for iPod-style Artist > Album browsing
I'd like to add to the chorus of folks who seem to think Spotify for iOS is a great start, but is missing some key features. The gaping hole in the mobile experience is that browsing for a specific album or song is incredibly cumbersome: you have to search by typing the name of the artist, album or song. (Sure, you could make a playlist for every album in your collection, but with a large library that would become unwieldy.) A scrollable list like the iPhone (and iPod Touch) has for Artist > Albums > Songs is absolutely essential.
Adding a "Library" icon on the tab bar at the bottom of the app is the first implementation that comes to mind which fits with Spotify's current design. This view would have the same contents as the Library in the Spotify desktop app, except in an iPod-style scrollable list with a drill-down structure of Artist > Albums > Songs. In "Offline Mode", the view would work the same except only containing content previously enabled for offline listening.
As a customer new to Spotify since its launch in the US, I see this as the key missing feature Spotify needs in order to create an experience that rivals and could potentially supplant iTunes.