You shouldnt pass up Ghost in the Shell so easily. Dont watch the film watch the series for starters. And give it a good half dozen episodes before you throw it away because of the cyber punk, and give it a dozen before you throw it away because of disinterest. The Laughing man story is seriously one of the most interseting intelectual narratives I have ever expereinced.
But from what you were saying, staying away from the main pitfalls of anime (cute cuddly sidekicks and kids saving the world).
Cowboy Bebop (has a pet dog but its really quite cool) - Pretty much Bounty hunters in space, sadly a reasonably short series, what is there is great, soundtrack is phenomonal and the characters are enjoyable.
Beserk - This is a set in a darkages european like world, and follows the adventures of a man named Gutts from birth. It is a fantasy land although there is little magic in the series, This is probably have to be the most epic story in all of anime if not most epic story ever told, the series will leave you wondering and you will have to read the manga to find out what happens next, but it is certainly a good watch.
You should note that Marval have begun making their superheroes into anime, Iron Man has been done and Wolverine is being released atm. they are interesting takes, if funny looking takes on Logan and Tony Stark.
Psychological animes.
These are what i think are the more mature of the animes out there, focusing around battle of wits more than whose sword is the bigger or whose magic is stronger.
Death note - Think Dexter but where killing bad people is 100x more easy so he kills 100x more people... thats probably pretty bad analogy. The art is amazing, and the mind games that are played are enjoyable.
One Outs - You dont like baseball? well you do now! watch the first episode and try not to watch anymore.
Akagi - An anime set around gambling, specificaly mahjong.
Kaiji - another anime set around gambling, this time many different types of gambling, such as scisors paper rock... sounds boring, but you would be surprised, the insight into the games nad the ways people can play is rather interesting.
But from what you were saying, staying away from the main pitfalls of anime (cute cuddly sidekicks and kids saving the world).
Cowboy Bebop (has a pet dog but its really quite cool) - Pretty much Bounty hunters in space, sadly a reasonably short series, what is there is great, soundtrack is phenomonal and the characters are enjoyable.
Beserk - This is a set in a darkages european like world, and follows the adventures of a man named Gutts from birth. It is a fantasy land although there is little magic in the series, This is probably have to be the most epic story in all of anime if not most epic story ever told, the series will leave you wondering and you will have to read the manga to find out what happens next, but it is certainly a good watch.
You should note that Marval have begun making their superheroes into anime, Iron Man has been done and Wolverine is being released atm. they are interesting takes, if funny looking takes on Logan and Tony Stark.
Psychological animes.
These are what i think are the more mature of the animes out there, focusing around battle of wits more than whose sword is the bigger or whose magic is stronger.
Death note - Think Dexter but where killing bad people is 100x more easy so he kills 100x more people... thats probably pretty bad analogy. The art is amazing, and the mind games that are played are enjoyable.
One Outs - You dont like baseball? well you do now! watch the first episode and try not to watch anymore.
Akagi - An anime set around gambling, specificaly mahjong.
Kaiji - another anime set around gambling, this time many different types of gambling, such as scisors paper rock... sounds boring, but you would be surprised, the insight into the games nad the ways people can play is rather interesting.