1. Red Hot Chili Peppers -- One of the first bands I ever got into way back in 7th grade. Fantastic songwriting and just a solid band that works so well together. I've seen them live 3 times with my best friend from middle school. Just a little bit on the cheesy side sometimes, but I can't imagine life without these jams.
2. The Beatles -- I don't listen to them much anymore honestly, because I just wore out those records lol. But their influence on pop music is undeniable, their songwriting and craftsmanship impeccable, and again: worked so well together as a band. Broke up tragically too soon. Imagine how the world of music would have been had they stayed together longer. We got some good solo material from Lennon & Harrison thereafter, though Paul McCartney's material really took a nosedive with Wings IMO. Lol.
3. Linkin Park -- Guilty pleasure, but I'd be lying not to have them on this list. Another very early discovery of mine. Hybrid Theory & Meteora kept me alive during middle school. Chester's voice is legendary (R.I.P.). I consider this band to be the Bon Jovi of Nu-Metal due to their songwriting talents and longevity after the rest of the scene kind of died.
4. Pink Floyd -- Oh my goodness. Definitely wore out these records. This band really found that perfect blend between progressive rock and classic rock. Roger Waters was a big influence on me intellectually for his lyricism and political outspokenness. David Gilmour's guitar work is out of this world. Like the Beatles, I wish they could have stayed together longer. Some good solo material put out by them afterwards, but nothing like the quality of their classic period.
Oh my, already at 4. VERY TOUGH DECISION COMING UP...
5. Rush -- Damn. I guess it's gonna have to be Rush. Super intellectual and thought-provoking band. Incredible musicianship. I don't know how Geddy Lee does what he does on bass and still holds down the singing. Or how Neil Peart drums any of his parts for that matter. Utterly irreplaceable and unique band. Good on them for staying together so long.
Honorable mentions: The Rolling Stones, System of a Down, Dream Theater, Tool, Led Zeppelin, The Clash, Queen, Bon Jovi, Nightwish, many others.