What is Last FM?

Wikipedia gives a pretty detailed definition for what Last FM actually is.

Last.fm is an Internet radio station and music recommendation system that merged with sister site Audioscrobbler in August 2005. The system builds a detailed profile of each user's musical taste, showing their favourite artists and songs on a customizable profile web page, comprising the songs played on its stations selected via a collaborative filter, or optionally, recorded by a Last.fm plugin installed into its users' music playing application.

Recommendations are calculated using a collaborative filtering algorithm so users can browse a list of artists not listed on their own profile but that which appear on those of others with similar musical tastes. Last.fm also permits users to manually recommend specific artists, songs or albums to other users (as long as the recommendation in question is included in the last.fm database).

Here we have two very different ways of personalization. In contrast to Pandora, Last FM actually recommends music based on other people's tastes (a type of collaborate filtering). Sites like Last FM which make recommendations according to what other users are engaging in tend to be the more common kind of web personalization. Both are part of the phenomenon, and interesting to analyze and understand.