Seems like this has turned into a "who's your favorite band" rather than "best band" thread. I'll include both here.
I believe that the Eagles are probably the best band ever. Just insane for many many reasons already covered here.
Now, my FAVORITE band of all time is Staind. Staind's music has matured and evolved as their lives have changed. Their music is undeniably honest, edgy and a real look into Aaron Lewis's screwed up mind. His voice is the strongest male voice I've ever heard, bar none. Best of all, they're REAL people. They aren't "rock n' roll", Aaron plays golf every day, then rocks hard every night. Nicest guys I've ever met. I could go on and on.
Other great bands:
Sevendust
Alice in Chains
Tool
A Perfect Circle