Okay let us begin:
First, don't watch Dragonball... people say its good, but they're wrong.
Second, the same applies to InuYasha, Yu Yu Hakusho and Sailor Moon.
Third, when people say Shinji is an annoying whiner they probably don't take into consideration that he was abandoned by his father, is seriously afraid of him, has something that could be described as a minority complex.
Fourth, RahXephon is a NGE ripoff no matter what people say, although its not bad.
Now:
Utawarerumono - The One being sung
The story is about a mysterious person, wearing a mask he cannot take off. One day he wakes up in a village, saved by a young native girl. (Native here means she has a tail

)
As the story goes on more mysterious and mysterious things start to happen, and as you might have guessed in the end our protagonists true identity is revealed both to us, the audience and himself.
Busou Renkin - Arms Alchemy
The young protagonist happens to die in the very beginning of the story. Although it is so shocking that he does not believe it at all, the fact that he was brought back to life by a young schoolgirl with unfamiliar uniform. Later on he comes to believe what happened, after seeing a teacher turn into a snake probably 10 or so meters tall... who wouldn't lol.
Gantz
This anime is a simple and very obvious gorefest for those that like such things, it has no real substance except for moralising through the whole anime. Elfen Lied style violence but without a story.
Gungrave
Now this one is damn good, its a mob story in the near future. In a city ruled by the organisation Millenion. Our protagonists, a bunch of lowlifes try to survive the waves of crime as they can... but somehow they get involved with the above mentioned Millenion, ruled by Big Daddy, the righteous head of the local mafia, very much Vito Corleone style. Although it doesn't sound like it, its a very serious and touching anime. You might say it isn't, that there's no romance almost. It doesn't really have a happy or sad ending.
But please note: Gungrave is the MOST heroic anime ever made in the whole existence of multiplication i swear. Those who seen the anime can tell you all. Its probably the one and only anime that ever made me shed tears in bigger numbers. And before you start asking weird questions after watching it, no im not gay, nor are the characters in the anime, there's no such thing involved.
D Gray Man
Okay, now this world is a bit grotesque. Our hero Allen Walker is an exorcist, exorcists in this world are members of a weird clerical order, namely The Black Order, which hunts down evil beings created from the Dark Matter once brought back to a false life by their suffering loved ones they left behind. Our exorcists must also collect shattered pieces of Innocence which is said to hold the power to defeat the evil itself, the Millenium Earl.
Very intersting i must say, although its ongoing at the very moment.
I will continue these later.
As for what i think about longer series:
Well you see Bleach and Naruto really aren't that bad, but please keep in mind, that they aren't very meaningful at most times, and the emotions the characters have are often unrealistic as well, compared to other anime that is. Also, they never stop to get stronger, somehow there always will be a new type of spell, technique, hidden power or something among these lines that will make them uber strong compared to everyone for a couple of episodes, and this never stops. There often will be fillers, so they won't leave the manga behind. Don't get me wrong, im watching them as well, but if you don't have the time for them, to start watching like 350 or so episodes if you're gonna watch both, than don't.