I believe the reasons they were so successful had to do with four things: 1) They had several band members who could write great songs. 2) Several band members could sing lead (none better than Glen Frey), which gave the band different sounds so it wasn't monotonous to listen to them (i.e. New Kid in Town, Hotel California, Life's Been Good to Me). All of these hit songs were sung by different members in the band. 3) Joe Walsh. Not only could he sing and play a variety of instruments (he's mind blowing on electric guitar), his facial expressions while performing are mesmerizing. 4) The group's harmonies were almost as rare as The Beach Boys.
After more than 40 years they're still performing, which I find amazing. My IPod is filled with their hit songs. Here's to The Eagles, one of the greatest bands in our lifetime.