You criteria is a bit vague, but not too hard to satisfy, considering how much anime is out there of every kind...
Let me see here...
Twelve Kingdoms. One of the best anime series I have ever seen, and you can't accuse it of any of the things you are complaining about.
Maybe the Crest of the Stars/Banner of the Stars series. Character designs lean toward the cute, but it is a serious story about war set in a very scifi universe. Very good depictions of tactical space combat.
Fullmetal Alchemist is just good. It has some of the standard anime visual quirks in the comedic moments, but it isn't excessive, and the series as a whole is fantastic and dark.
Gankutsuou: The Count of Monte Cristo is another great.
Gungrave is a great mafia anime. It leans towards extreme action (with monsters and such even) towards the end, but it never loses great characters and a deep plot.
Wolf's Rain can be a bit strange, but it is also excellent.
Hmm... I keep submitting a post, walking away, and thinking of a new title. Maybe I should stop before I edit this post too much...