@Didymos Thomas,
There are three bands I would put as most influencing me.
In no particular order:
Led Zeppelin
Led Zeppelin is a very famous and possibly overrated band. As far as their complexity and such things, I know nothing. However, they are very good. What I find inspiring in Led Zeppelin is their extreme variety. You can look at their "Immigrant's Song," which, along with "Kashmir" and "In My Time of Dying" is their best examples of hard rock music. They also have experimented with reggae themes in "D'yer Ma'ker" and "The Crunge." They have the capacity to make slower and extremely beautiful songs such as "The Rain Song", "Ten Years Gone", and "All of My Love". Also, references to Tolkien's fantasy, like in "Misty Mountain Hop", "The Battle of Evermore", and "Ramble On", really endear them to me as I am a total LOTR nerd. Their wide talents in many different sounds really makes Led Zeppelin stand out to me.
Emerson, Lake, and Palmer (ELP)
Well, first off my avatar on this forum is the cover art for their album
Brain Salad Surgery. I like ELP because they, like Led Zeppelin, have a wide variety in their music, ranging from Emerson's Piano Concertos to the sad song "C'est La Vie" to the reworking of classical music on their
Pictures at an Exhibition album, to their cover of Aaron Copland's "Hoedown" to their epic song "Karn Evil 9". Not to mention that all three musicians in this band have amazing technical ability in their respective instruments.
Jethro Tull
Jethro Tull is amazing, with their fusion of jazzy tunes and melodies conjuring up pictures of old castles and medieval themes. "Thick as a Brick" is one of the greatest songs ever written, in my humble opinion, for it is an epic, sprawling piece extending over forty minutes. Also, they put a lot of thought in their albums. "Thick as a Brick", for example, which took up an entire album, had an entire backstory involving a fictional boy who was said to have penned the lyrics of the song as a poem for a competition. They wrote an entire fake newspaper for the cover of that album. Not to mention that they named themselves after an English agriculturist. I mean, how cool is that?
Cream
OK, I lied, not three. I like Cream due to their bluesy take on psychedelic music. I really like the kind of distorted images that psychedelic music puts in my head (although I do not support or use psychedelic drugs or any drugs. I find enough mind-expanding psychedelia in music like Cream, Jimi Hendrix, and Pink Floyd) Their song "White Room" especially has had a profound effect on me.