You know, I never understood the love for Gurren Lagann. It's not bad at all, but people worship it with such passion. Perhaps it's one of the gateway shows for the new generation? Like Dragonball Z, Trigun, Love Hina, Evangelion, Ranma 1/2, Cowboy Bebop, Saint Seiya, Sailor Moon, etc was for my generation?
Gurren sacrifices... well, it sacrifices its ability to be taken completely seriously by me. Sure, there's sad moments, and in proud, oldschool Gainax tradition, the ending is all fucked up and depressing as fuck, but by going for that oldschool 70s Super Robot, Burning Youth/Passion/Friendship thing (like the original Aquarion show, or Nadesico) it kind of creates a distance between you and the story. It's style over substance. Kind of like Kill Bill, Inglourious Basterds. Sure, they're great movies, but it won't affect you the same way a Shawshank Redemption or a Grave of the Fireflies does. Perhaps it doesn't have to... I don't know.
As for Evangelion, complaining about the complicated, insane, or gibberish-filled story means you are kind of missing the point. Eva is in many ways a descent into madness, and the style in which the show was made helps the show to drag you down into that madness.
And Dragonball Z... I think it has pretty much been said already. Technically a good show? Probably not. But it's fun nonetheless, and for a vast majority of older anime fans it was one of those, if not THE gateway show that introduced this wonderful and horrid world of anime to us. You could perhaps compare it to Harry Potter, in how Harry Potter, being far from a perfect series of novels, introduced the love of reading to so many young people.
As far as new shows are concerned, I kind of agree with DJ66.
Moreoever, the reason most suggested "gateway" shows are so old, is because anime has changed a great deal. More and more, anime has become targeted at that small niche of japanese otaku that prefer fanservice and mind-numbing cliché over content and innovation. Because it's usually those crazy otaku that obsess over a certain female character's virginity, or perfectly-shaped bosom that spend the most money on the merchandise.
The same way mainstream western horror movies have slowly been gravitating towards "torture porn" the likes of Saw, Hostel, etc (which was almost exclusively the domain of exploitation horror), anime has been gravitating towards the grotesque forms of fanservice.
Ranma 1/2 had boobs and panties in every other frame, but the story didn't linger on them, it was usually mostly a comedic device. Anime nowadays almost exclusively focuses on the perverse.
One of the last shows I really really liked was Bakemonogatari, even though it had its fair share of loli, nudity, sexual innuendo, etc. At least it was done with some dignity, and when it sometimes strayed from that line, the witty dialogue was always there to keep our mind focused on the story, and not the luscious, rounded shapes of the female characters.
Its sequel, Nisemonogatari, I've only watched a few episodes, is already straying very far from that line, and even though the animation is gorgeous, and it's very sexy, I can't help but regret the direction it went (though I have never read the novels).
I won't go all oldfag and say anime is dead, but I sure miss the older shows.
PS: Naruto is cool lol?the manga anyway. Nothing wrong with brainless shounen fighting anime. And it's pretty much still an oldschool show.
Edit: Oh, btw. On the topic of Evangelion being copied to death; some of those copies are pretty damn amazing in their own right. Rahxephon, for example (early BONES). When watching Rahxephon, I'm hard-pressed to say Eva is better. The style, design, music, voice acting, atmosphere... in many ways it IS better than Eva (in others it's not). Even if the similarities between the stories are glaring, you don't really pay much attention to it while watching.