Probably one of the main criticisms of TTGL is that it's a big storm of cliches. I'm not saying it isn't, but I am saying that it's justified. Different ways of looking at the show can yield different reasons, but as a whole I firmly believe TTGL is cliche for a reason.
GURREN LAGANN AS ITS OWN SHOW
No doubt most of us have seen at least one mecha show before TTGL. Given that it's Gainax, it's plenty likely that we've all seen Evangelion as well - we'll get to that angle later. When it aired in Japan, TTGL started on April 1, 2007 - a Sunday, and in a morning timeslot. For all intents and purposes, TTGL was the equivalent to a Saturday morning cartoon. Younger kids who would not be as exposed to mecha anime like Gundam or Evangelion would be watching it. The crude type of humor in Gurren Lagann shows this very well - most of it tended to be fanservice jokes or people getting grossed out by Leeron's supreme gayness, stuff that younger kids might find funnier than us older folk would.
Remember when Mighty Morphin Power Rangers started airing in the US? I was a bit too young to remember everything well, but it was a pretty new concept. In Japan, it was called Kyōryū Sentai Zyuranger, and it was the SIXTEENTH version of Super Sentai. But to American audiences, it was the first, and we ate it up shamelessly, even if it did follow the whole Sentai formula to the letter.
It was a similar deal with Gurren Lagann. Kids who were most likely unaware of all the cliches and character archetypes that had been permanently etched into the mecha genre were watching this show. TTGL was exposing them to all of that. You wouldn't call something cliche if it was the first time you saw it, even if long-time watchers of the genre as a whole would.
GURREN LAGANN AS THE ANTI-EVANGELION
Gurren Lagann came out some ten years (give or take) after Evangelion did, and given that they're both made by Gainax, it's inevitable there would be comparisons and contrasts.
To look at TTGL from this angle, we have to look at Evangelion first. NGE took all the cliches of old Super Robot shows, and turned them on their heads. It was completely formulaic at first glance - ordinary high school dude ends up piloting a super-powered mecha designed by his long-gone father, and becomes the last hope of mankind against an alien threat.
But then we see what happens when you take a 14-year old kid and use him as a child soldier. We see just what kind of father would abandon his family to create a mechanized weapon. We see the traditional character types of old mecha anime (the hot-blooded character, the stoic character, and the cowardly/shy character), but they're all taken and followed through to the logical conclusion of how messed up people who act like this would actually be in reality.
Evangelion was a massive hit, as we all know, and it revolutionized the mecha genre. Instead of imitating things like Getter Robo, everyone started imitating Evangelion. What was a complete deconstruction of the cliches of mecha anime now became the standard. TTGL took what had been established in the decade since Evangelion, and turned THAT in its head.
Simon starts off just like Shinji, only he has Kamina backing him. Eventually, he becomes practically a whole different person - he rises up where Shinji fell, and comes to terms with what has to be done and the fact that he's the only person who can really do it.
Yoko is the anti-Asuka. This is perhaps best shown near the beginning of the series, where Simon accidentally lands on top of her and gets a facefull of her cleavage. If it were Evangelion, Simon would have surely received a fist or two for his bad luck, and probably brooded about it for a while. Yoko smiles as the flustered Simon apologizes - she understands it was an accident, and that there's no reason to be all upset and in his face about it. She's still the red-headed action girl, but she's not the complete jerkass tsundere. By the end, she's completely rejected Simon's affections, but they remain good friends and there's no real sexual tension between them afterwards.
Nia is the anti-Rei. Where Rei was stoic and emotionless, Nia is peppy and expressive. They're both willing to charge into suicidal situations, but for different reasons: Rei knows that there's an aquarium of replacements of her, that she's just an expendable element, but Nia has the utmost faith that Simon and the rest of them will come to her rescue. The final leg of Evangelion is kicked off with Rei's death, as Shinji's attachment to her causes him to become even more depressed and withdrawn - Nia's capture by the Anti-Spirals and Simon's love for her is what kicks off the last leg of Gurren Lagann, but the separate thematic development of both shows causes each of them to go in completely different directions.
So, from this view, Gurren Lagann is cliche, but because it takes the newer cliches and flips them back around to be closer to the older cliches. Still, it's obvious that both play a role in how Gurren Lagann develops, and as a result TTGL seems cliche. Instead of NGE's broody feel, we get back the hotblooded feel of stuff like Getter Robo.
GURREN LAGANN AS A LOVE-LETTER TO THE ENTIRE MECHA GENRE
Gurren Lagann mirrors the development of the mecha genre as a whole, making it incredibly cliche.
The focus at the beginning of the series is definitely Kamina, even if Simon is the viewpoint character and the protagonist. He constantly spouts phrases like "Believe in me who believes in you!" and is utterly convinced that love and spirit and whatever powered up emotion will drag everyone through. How do you pilot the robots? With fighting spirit, nothing more.
This mirrors the old super robot shows where glowing green energy and hot-blooded protagonists were all that were needed to win the day. Did you need to plan? No, because as long as you tried hard enough, everything worked out. And indeed, during the first segment of TTGL, determination and trust is what carries everyone to victory.
Then Kamina bites it, because Simon gave into despair for a few moments.
From there on, everything about the hotblooded determination becomes a bit downplayed. The characters know that's how the world works now, and they follow this dogma instead of shouting it loud and clear. The tones are there, but they no longer take center stage, until the climax of that arc. This reflects the use of cliches - people are aware that there are cliches, and that they're used, but they're not played completely straight and seriously anymore. There's deviation, changes, subversions of the formula, but the formula still exists.
By the third leg of the show, after the timeskip, Gurren Lagann as a mirror completely reflects the Evangelion era of mecha shows. Sheer hot-bloodedness and determination doesn't help our heroes now, or at least not nearly as much. Though up until now all mecha have had expressive faces, the new enemies have none. They arrive and destroy, and are only defeated by turning their own beams against them.
Even the allied robots, the Grapearls, are all copies of the Gurren-Lagann, mirroring the follow-the-leader mentality of mecha shows after Evangelion. When the rest of the Dai-Gurren Brigade says they'd be able to defeat the Anti-Spirals in their old mechs, Rossiu vehemently denies them, saying that the newer Grapearls are superior. The old mecha were remnants of an older age, "unsuited to the modern era". TTGL as a whole has a darker edge during this segment. Rossiu's logic fits a real robot show far better than a super robot show. The Giga Drill Breaker is used offscreen, completely defying the rules of the genre.
EDIT: Stilts brought up a good point in his comment below: "The solution to virtually every problem in the third act of Gurren Lagann is to use more fighting spirit and/or create a bigger and better weapon."
This is true, but their solutions keep leading to further problems for Simon. Destroying the first Mugann causes further collateral damage to Kamina City, and only by working with the copied Grapearls can Gurren-Lagann defeat the second wave of Mugann. Soon after that, with the Giga Drill Maximum, Simon overextends himself and cannot defeat all of the Anti-Spiral enemies - the Grapearls arriving with their new tech is what saves both Simon and Kamina City. The third act's despair hits its peak as Simon and the ideal he embodies is imprisoned, and Rossiu takes it upon himself and his ideals to save humanity.
By the final few episodes (40%!), Gurren Lagann is its own being. It took everything from before and poured it all into a blender, driving up and beyond everything done with older shows.
The main symbolism of TTGL is in the form of a drill, moving ever forward. There is constant mention of breaking down barriers that stand in the way, and the memory of Kamina drives the characters. At the end of the series, Simon says that he's done digging a hole, and that it's time for others to go through the hole he's dug. This is the meaning that TTGL has built up to - they mirrored the entirety of the mecha genre, using the holes that had been dug by other series and studios. They moved through them, and at the end when reason is completely ditched and everything is so over-the-top as to become nonsensical is when Gurren Lagann is digging its own hole. The new hole for new mecha shows to go through.
So, in the end, is Gurren Lagann cliche? Hell yes it is. The characters are all completely archetypal and formulaic, and the show manages to pull it off amazingly, with multiple levels of meaning. Of course, don't just take my word for it - come up with your own conclusions, and feel free to disagree. This is just what I left Gurren Lagann with, among other thoughts that don't fit the theme of this post.
So remember, Believe in the you who believes in yourself!