The 1970s
Pink Floyd
Easily the most commercially successful prog rock (or space rock for you nitpickers) band from this era but they truly redefined what a studio band was. Studio bands started awhile back with The Beach Boys (Pet Sounds) and The Beatles (Sgt. Pepper) but Floyd made it an art form. They're probably one of the first bands that you could truly label as artists because of meticulously crafted their works were. Instead of hard hitting rock and roll they often slowed down and let the music build and ebb and flow, something I'm not sure anyone else really cared to do before this time, at least on the level Floyd did.
Black Sabbath
Who would've thought one little metal shop accident would've changed the course of rock music? With Tony Iommi determined to make his guitar playing a little easier he down-tuned simple blues rock and ended up created a menacing sound that, which resembling more doom metal than heavy metal, scared enough parents to make their mark on the world. Everything that is heavy metal can be found in Black Sabbath: dark themes, down-tuned guitars, heavy distortion (for the time it was heavy), dissonance. While not the true masters of their craft they were one of the first, if not the first, dark band to break through and create a real interest in the type of music they played.
Led Zeppelin
It pains me to list Zeppelin here only because I like The Who better but I can't deny the hard rock explosion they ignited. Many call them the start of heavy metal but with bands exploring actual dark themes like Black Sabbath I simply cannot do that, though they turned blues rock into something much more rhythm driven and heavy hitting. Page also perfected the art of riffing as he created (or stole if you wanna go down that route) dozens of riffs that you'd instantly recognize upon hearing two or three notes from. Truly a unique band and along with The Who transformed the art of performing on stage instead of just playing the music.
The Ramones
Why not The Clash or The Sex Pistols? Well you see kids the reason those two bands actually got around to playing music is because they learned to play their instruments by listening to The Ramones (true story). They started the punk rock look, the punk rock attitude and the punk rock life style. The Sex Pistols might've taken it and "perfected" it but ask any member of any of those bands where it all started and they'll point you to The Ramones.
The 1980s
Metallica (with slight nod to Dave Mustaine)
For all you purists out there I included Mustaine only for the fact that he and Hetfield either crafted or heavily modified the art of duel guitarists for pretty much every single band to try metal since Metallica's inception. Naturally when Mustaine left Hammett and Hetfield perfected that art. Since then, the influence they've had on any number of bands is startling. It's true that Metallica and thrash are more American styles to their British speed metal brethren but what they did with virtually no radio or media exposure is astounding.