"Don't believe in yourself! Believe in the me who believes in you!" Explanation
Many of Kamina's phrases are repeated/modified for the inspiring hamminess, this one often with "me" replaced with something else. Other examples are listed below.
"Your drill is the drill that will pierce the heavens!" *
This might actually have gotten a reference in the soundtrack - one of the songs is called "Omae no XXX Ten wo Tsuke!" or "Pierce the Heavens with Your XXX!"
"JUST WHO THE HELL DO YOU THINK I AM!?" *
Alternatively "Are you aware of who exactly I am?!", due to Nia's Japanese Politeness.
Shopping Kamina's Cool Shades, or even Simon's weird-ass star-shade-goggle-things, onto a character makes them instantly badass, or even more badass, as the above image demonstrates.
Simon's response to Nia's claim that as long as the success chance isn't exactly 0, it's as good as 100% to him. Embodies the characters' habit of surpassing all expectations, even if physics itself is against them.
8:52 is the hour that real men go beyond all known laws of reality, become heroes, and ascend to the realm of GARhalla. Explanation (spoilers)
Used in reference to Kittan's Heroic Sacrifice with Libera Me From Hell blasting in the background. His big moment started at approximately 8:52, and his final moments were just seconds before 8:53 on the timestamps. Kamina's Dying Moment of Awesome also occurred at around 8:52 of episode 8.
A British poll to change the country's flag (currently the Union Jack) that allowed people to submit their own flag designs. The winner was the Union Jack with the Dai-Gurren logo superimposed in the center.
For that matter, along with Sorairo Days, Ten wo Tsuke, Happily Ever After, and Libera Me From Hell are also known to be favorites to superimpose over a Crowning Moment of Awesome. For greatest effect: Ten wo Tsuke should come when you're going to pull off something completely awesome. Happily Ever After should be used after recovering from a Heroic BSOD (Or a similar moment that makes you shout "He's back!". And Libera Me From Hell should be reserved only for those about to enter the illustrious halls of GARhalla in an ultimate Heroic Sacrifice.
"My bro is dead, HE'S GONE! BUT! He's here in my heart, and on my back, he continues to live through me! If you're going to dig, dig to the heavens! Even if it means my grave, I'll dig through, once I did THAT MEANS I WON! Who the hell do you think I am?! I'm Simon, I'm not Kamina's little bro. I'M ME! SIMON THE DIGGER!" Explanation (spoilers)
After Kamina's death resulted in Simon spending several episodes in a Heroic BSOD to end all BSODs, with this speech he performs a spectacular He's Back moment that swiftly became legendary.
Norio Wakamoto doing his interpretation of Giga Drill Breaker. There are at least three different You Tube videos featuring this voice clip with various comments on its "manliness". Common interpretation of the *beep* in the middle is that the uncensored version would annihilate the speakers and everything near them.
Someone decided to make a pun regarding the character Viral and the term "viral marketing". Cue endless drawings of Viral in a business suit.
Referenced by at least one fansub: "This is a free fansub! Not for sale, rent, eBay or beastmen!"
Simon is such a bad ass that he defeated the big bad with essentially his car keys is gaining popularity. It started on this wiki, reached a Youtube video of the Simon vs. Lordgenome fight, and will start to speed up.
Yelling "FINISHING MOVE!!!" gives the Giga Drill Breaker its power. Explanation (minor spoilers)
During the fight against Lordgenome, when Simon tried a Giga Drill Breaker, he didn't yell "Finishing Move" beforehand, and Lordgenome deflected it. That probably wasn't the actual cause, but who knows?