Mighty Morphin' Power Rangers, the first iteration of the franchise, is where a lot of the original songs in the franchise can be found, most if not all from this era done by composer Ron Wasserman. In his History of Power Rangers videos, Lewis Lovhaug refers to the "Wasserman factor", whereby awesome music can enhance the viewing experience of the show.
First and foremost is MMPR's famous theme song "Go Go Power Rangers", featuring both epic guitar riffs and catchy lyrics that are guaranteed to get stuck in your head.
Surprisingly, while most of the show is supposed to be kind of a comedy (and even if it's not an outright comedy, it's very, very campy even at its most serious), the first three seasons had a very epic soundtrack, spearheaded by a theme song that becomes doubly epic in season 2 when the extended version is revealed, and has actual lyrics. All of this, alongside a robotic Asian dragon, Serpentera, weaving through stormclouds. The debut of the Ninja Zords did it one better... with a second verse.
"And we keep dreaming of a world where all was good as we were told, We Need a Hero." Any old routine putty fight of the show, set to this music, becomes less obligatory and more awesome just by being set to it.
"Tenga Bye Bye" is awesome music set to bizarre lyrics (to be fair, the Tengas were kinda ridiculous to begin with). It all combines into something really cool.
If Ron Wasserman is the king of Power Rangers music, his successors, Jeremy Sweet and Jim Cushinery should be nominated for a close second. They created their fair share of awesomeness as well, such as "Big Bang" and "Invincible"
You think the original theme was good? Try listening to it when it's being covered by MASAAKI ENDOH!!! Your head will explode from the epicness.
Thought Lord Zedd's theme from the show was awesome? Wait till you hear the extended version!
Not only was "Go Go Power Rangers" used to build the theme for Zeo, but a few chords are borrowed for the non-theme song "New Rangers to the Rescue" which debuted in Turbo. The first two teams of the new Saban era, Samurai and Megaforce have their own remixes of "Go Go Power Rangers" used as their theme song. All awesome.
Power Rangers Dino Fury's theme song is somewhat controversial due to the techno music contrasting with the mystical dinosaur theme, but it's generally agreed that whether or not it contrasts the subject, it sounds awesome, and the score in general is considered one of the best thanks to Bert Selen. Dino Fury...
", featuring both epic guitar riffs and catchy lyrics that are guaranteed to get stuck in your head.