Greatest Hits

Have you ever discovered a new band and thought to yourself, "How do I not have any of their music?"  But what happens when the band has over five albums with their hit singles spread across each record?  This is where a greatest hit album or singles collection comes in.  Many well known artists releases these.  Some of the most recent being Fall Out Boy, Britney Spears, and Madonna.  They are usually considered the artists "very best".  The question is, do you buy it.  I always have a problem with this decision.  When I acquire a sudden interest in a band, I face the dilemma.  The problem is, what if I do buy this compilation but then want more of their music.  I'll already have bits and pieces of their catalogue, causing me to buy songs that I previously bought.  I don't want to buy the same song twice.  With this being said, I do own several "Greatest Hits" albums; artists such as Nirvana, The Ramones, and The Clash.  I guess the answer to the question is another question.  "How much do you really like their music?".  Can you live without all of their music, or do you need all of it?