Wow, I could spend days on this, but I wont.
1. New Order
They put out some of the best music ever between 1980 and 1989. I know everyone always counters that Joy Division are better, but I dont, nor will I ever buy it. They were not only groundbreaking and influential, but wholly entertaining and moderately commercially succesful, while never losing a touch of integrity. Add that to the gorgeous visual art that was their album covers and its just hard to beat. Plus if you cheat and add all of the side projects, Electronic, Revenge, Monaco, and the Other Two, there is absolutely no question, and this takes care of the 80s and 90s.
2. Echo and The Bunnymen
Once again people are going to argue that their early stuff was so much better, but they put out two fantastic albums in the 90's; What Are You Going to Do With Your Life, and Flowers. Add these to their already impressive catalogue and you have a fantastic canon.
3. Love and Rockets
They made a fantastic transition from post punk goth in Bauhaus all the way through transcendental rock with Express through smooth pop with their eponymous all the way to fantastic electronica with Lift in the late 90s. A wonderful ride by a wonderful live act.
4. The Trash Can Sinatras
Probably the very best underappreciated band of all time. It is fantastic pop music with incredibly tight arrangements coupled with intelligent, witty, and wistful lyrics with incredible sounding recordings to boot. Their three albums Cake, Ive Seen Everything, and A Happy Pocket will stand up to ay three albums put out in the 90s. Period. If you have never heard them, do yourself a HUGE favor and visit trashcansinatras.com or email me for a compilation.
Everyone else is tied for 5th, hehehe