Most of what you're likely to have seen, turtlebird, comes from a genre of anime (that's right: genre of anime; anime is not a genre in and of itself) known as shounen. That is, anime marketed towards young boys. And your stereotypes are largely correct, as far as that genre goes (though not always; I recommend Boys Be for an example of shounen anime which breaks the mold).
Shoujo anime, which is marketed towards young girls, tends to be very different, and would probably be more to your liking. While you'll find some "severely gendered" characters, you'll also be introduced to The Wonderful World of Bishounen, who pretty much obliterate most Western gender stereotypes out there, and then invent a few new ones so they can break those too. Indeed, there are many other character archetypes seldom seen in shounen which break the stereotypes, but I note bishounen as the most famous of these. The humor tends to be more subtle, and the characters more developed than in shounen (well, mentally developed, at any rate; they aren't as physically developed in shoujo, but I get the feeling you'd prefer this anyway). The story tends to be driven more by characters and the relationships between them, rather than the plot; this is a matter of personal taste.
Shoujo isn't for everyone, of course. But then, neither is shounen. If you don't like shounen anime for the reasons you've stated, then I'd consider at least giving some good shoujo a try. A good one to start with is Marmalade Boy, though I must warn you that it's very long.
it's sad to see someone see only one genre of a medium and mistake it for the medium itself. It happens, though; see Sailor Moon and its ilk are not anime for another example of this. But this is exactly the problem anime fans have with explaining their hobby to others; people see one genre -or worse, go off the prejudices they have about cartoons being for kids- and think all anime (or the vast majority) is like that.
OK; it's obvious that this is causing some controversy. Would the downvoters please be so kind as to say why?