I would have to say looking at impact on the music scene my choices are the Beatles and David Bowie. Their impact is felt on almost all genre today.

Beatles and David Bowie

The Ramones and The Who.
It's hard to leave out bands like Led Zeppelin or Credence Clearwater Revival though.

Can't think of two, but David Bowie. Go listen to some of the stuff off his last record. Amazing to be that creative at that age near the end of his life. Holds up against any of his stuff from when he was younger.

Bowling For Soup and The Asteroids

The Who & Pink Floyd....

The Dixie Dregs, and The Beatles. Honorable mentions go to Pink Floyd, ELO, Styx, Yes, Rush, Elton John, Billy Joel... jeese... too many to remember really..

Frank Zappa and Pink Floyd. Have been listening to Floyd recently, the real early stuff. Just listened to Atom Heart Mother.

Its a toss up between Pink Floyd, David Bowie, Jethro Tull and Trent Reznor...I know you said two but this is a complex question for me to answer. There are a plethora more that I can mention as well. There are just too many influences musically.

The Beatles were the most innovative and influential band in history. They not only changed the music, they changed every aspect of the music industry, from the way albums were put together to the size of concerts. No one will ever do that again.

Frank Zappa and Jack White.

Muse and Pink Floyd

Queen and Queen. Overdubbing and studio work was ahead of its time.

Way too many to state categorically that any two are the most innovative...

I am sure that Tiny Tim, John Cage, Laurie Anderson, Philip Glass, Monk, etc etc can ALL be classified as innovative, but does anyone actually ENJOY their music...

Having said this, it all renders down to personal choice...for me Bowie and Pink Floyd are right up there on that shimmering pedestal...closely followed by a whole raft of others...Gorillaz, Bjork, Roxy Music, The Doors, Marc Bolan, The Who, Dylan, etc etc...
I just re-listened to 'Meddle' by Pink Floyd this evening, and was totally transfixed with its freshness after all these years.

Linkin park and sugar hill gang

for their time the beatles put weird on the map and hendrix with chas chandler at the helm had us listening but now some of the drum and bass kids sure do light the way to say nothing of the sampling going on

I would nominate Nirvana and Alice Cooper.

The Beatles are definitely a given! The 2nd is hard. Bowie was a great pic that others have mentioned and would've been my pic. Since I was late on the Bowie draw, I'm going to go with Portishead! At a time when rock was reaching its creative end, and everyone was on the grunge bandwagon, they combined hip-hop, a live DJ, orchestrations, theremins, and their own unique rock into their own genre.

Radiohead and Explosions in the Sky

The Eurythmics, together or Annie only. Freddy Mercury et al.

The Bonzo Dog Doo Dah Band

Yes Bowie!!
Roger Waters

Nine Inch Nails.
Tool

Benny Goodman was the first to integrate black musicians in his band.

2Cellos
David Bowie

Innovative squared!