Who the Hell do you think I am!
Perhaps Fairy Tail might be up your alley, it is kind of the hotest Shounen anime at the moment (that is the genre Dragonball fits into), it is a big fantasy series. opening song
Full Metal Panic series is kind of semi-futureistic, kind of switches between millitary and school life comedy (sounds like a bad idea but works). Trailer
Spice and Wolf can be a good choice, it is pretty plot driven anime, and it does it well enough that it makes medievil economics very interesting. The dialogue is pretty brilliant, granted this not a series that you can just lay back and have the plot spelt out to you, you will have to pay attention, and a big problem will come in the shape of plot rather then some violent thug. Trailer (english)
There is always Death Note, very good but gets recomended so often. Maybe Durarara, kind of feels fresher, it is a kind of mystery plot driven story. Opening song
Tell you what, check out the recently finished Shinryaku! Ika Musume (Invade! Squid Girl), the plot sounds absolutly insane and like it won't work, but is very good, probably one of the best this year. It is a comedy and the plot might sound a bit crazy, especially since you asked for a plot driven anime, but quite a few people have come to the opinion that it is not the kind of show they will enjoy, then boast about how much they enjoyed it out of just curiousity, absolutly hillarious show. Opening song
Also recomend Ika Musume is that since you are just begining I recomend trying out different shows as you can be surprised what genre you might enjoy, I really never thought that I would like some of my favourite genres when I started a couple years back.
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Through dream I travel, at lantern's call
To consume the flames of a kingdom's fall