Any "Darth Vader vs. Adolf Hitler" match. The first has a significant improvement in musical and lyrical quality over "John Lennon vs. Bill O'Reilly", the second has the soundtrack of Van Helsing as its background music, and the third has some particularly memorable lyrics.
"NicePeter vs. EpicLloyd". That beat wouldn't sound out of place on a radio song.
"Mario Bros vs. Wright Bros". It sounds exactly like a soundtrack from a typical Super Mario game.
"Michael Jackson vs. Elvis Presley" manages to have a rather unique presentation: it starts with Jackson from his The Jackson Five days (meaning kid!Jackson) going up against Deliberately Monochrome 1950s!Elvis, before having Jackson become the Moonwalker and Elvis porking up.
"Cleopatra vs. Marilyn Monroe" has a very fitting Egyptian-themed beat behind it and it makes the rap battle that much more awesome.
Napoleon Vs. Napoleon has one of the best tracks ever, and the fact that the soundtrack is quite blatantly taking sides only seems to add to it somehow.
"Frank Sinatra vs. Freddie Mercury", which subtly includes the beat from "We Will Rock You".
"Bruce Lee vs. Clint Eastwood". While Lee and Eastwood's flow is great on its own, the dramatic backbeat is what truly ties the rap together, and it ends on the whistle from The Good, the Bad and the Ugly.
"Mohandas Gandhi vs Martin Luther King Jr.", the first rap to have Key & Peele as the rappers, and one of the only cases of a hard rap between two pacifists.
Thomas Edison vs. Nikola Tesla. "You did not steal from me, you stole me from mankind!" The beat and the lyrics flow well with each other almost better than all previous episodes. Plus, the beat almost makes the Battle sound like a Mega Man (Classic) game!
"Lance Armstrong vs. Babe Ruth" - The beat sounds exactly like what you'd hear in a serious rap song.
"Mozart vs. Skrillex". One of the best music beats in ERB, it combines dubstep with Mozart's music to create a seriously awesome beat.
"Blackbeard vs. Al Capone" can easily be used as a film or video game score.
"Michael Jordan vs. Muhammad Ali". Low notes on a sports organ, city-style horn section, and a groovy drum beat. Once again, the announcer is singing along at the end.
"Rick Grimes vs. Walter White" has a nice dramatic undertone, fitting considering who the combatants are.
"Goku vs. Superman" has a suitably epic industrial beat for a pair of Invincible Heroes, along with some of the best lyrics in all of Season 3.
The beat to "Artists vs. TMNT" is awesome.
"Ghostbusters vs. MythBusters". The beat is so tight that it goes great with the leitmotifs used for each side (a theremin for the Ghostbusters and the guitar chords fitting of the MythBusters). Oh, and the rap was good, too.
"Thor vs. Zeus" has an epic violin section and background synth that sounds like Ominous Latin Chanting. Certainly fitting of ancient gods.
"Jack the Ripper vs Hannibal Lecter" may have the most epic beat in the entire series, and it's even one perfectly suited to the two contestants.
"Steven Spielberg vs Alfred Hitchcock vs. Quentin Tarantino vs. Stanley Kubrick vs. Michael Bay" has five separate beats, something that Lloyd points out in the BTS. Each one is absolutely great. Special mention to the strings in Spielberg's verse.
Regardless of what you may think of the battle itself, there's no denying that "David Copperfield vs Harry Houdini" has a beat that's dark, eerie, and awesome.
"Terminator vs Robocop" has a loud marching and clanging score that fits the environment of the battle and the augmented rappers very well.
"Eastern Philosophers vs Western Philosophers" has one of the best beats in the history of the series, and is agreed to fit very well with the wonderful vocals. Also, this episode features the first instance of beatboxing in the series.
"Shaka Zulu vs Julius Caesar" has a very tense beat with war drums and violins, befitting the two contestants.
Minor note on "J. R. R. Tolkien vs George R. R. Martin": when Tolkien mentions Led Zeppelin, the band appears behind him and you can hear the beat change as a sort of reverse Diegetic Switch. It is awesome.
Just as in Spielberg vs Hitchcock, "James Bond vs Austin Powers" uses a different beat for each rapper that represents the tone and style of their respective movies. There's also an awesome Powers-style electric guitar solo in the end credits.
Fredrick the Great's intro from "Ivan the Terrible vs. Alexander the Great" is pretty awesome. And most of the lyrics of the final set are sung R&B-style. It's one heck of an enjoyable and well-performed change-up.
Stevie Wonder's first lines in "Wonder Woman vs. Stevie Wonder", sung instead of rapped and with a cool little jazzy/soul number on top of the beat from Wonder Woman's first verse.
Tony Hawk vs Wayne Gretzky has a great upbeat beat to fit the sports theme.
"Theodore Roosevelt vs. Winston Churchill" has an epic beat for an epic battle: a bombastic percussive march infused with orchestral brass and strings for Churchill's verses, and with electric guitar and ragtime piano for Roosevelt's. According to ERB Behind the Scenes, they used the hook section of their sample beat for the verses and faced a lot of difficulty putting it together. But they definitely made it work.
"Nice Peter vs EpicLLOYD 2" has possibly the most climactic beat used for a battle, complete with operatic chanting.