Most of my favorite bands are British (Bad Company, Fleetwood Mac(are they British or British- American?), Free, Def Leppard, Iron Maiden etc). The Eagles are the only band in my top 5 that are American. Given the fact that they are "the best selling American band of all time", I'm not surprised that most people rank them as #1, despite their personal feelings about the band. The numbers and the money don't lie.
The next band that comes to mind for me is Van Halen or Lynyrd Skynyrd. Aerosmith would be next.