Indie is a particular sound that has little to do with past associations of independent music. Indie also encapsulates a musical philosophy. Many artists utilize alternative instrumentation, jangling guitars, and may borrow from disparate genres such as folk, dance rock, and hip hop.
The term 'indie' is best known as being an abbreviation for the word 'independent'. This term was once used to differentiate between bands that were on a major record label and those that weren't. It also differentiates between an 'independent' sound and type of music and the more typical top-40 sound that was so prevalent during the 1980s. For example, many of the hair bands and hard rock scene had become very typical in musical composition (melody, chorus, melody, bridge, chorus, etc.). 'Indie' music may or may not follow this pattern.
For these reasons, in recent years the term 'indie' has been applied to bands that have rock sound but aren't on a major record label. Bands like Coldplay, The Killers and Razorlight are not classified as being 'indie' because of this. On the other hand, bands such as Radiohead (who are no longer on a major record label), Pavement, Belle And Sebastian, and Joy Division can be classed as indie using the "independent sound" meaning.
This term is wildly disputed on last.fm as well as on plenty of forums. People tag everything from Katy Perry to Meat Puppets as being 'indie'. You may even find some of your trve kvlt black metal bands appearing with an indie tag. As long as they aren't on a major record label. This spectrum of tagging shows the depth and arguably the inconsistency of the label.