Ohhhhh, this is one of my favorites - the nonpowered people in a superpowered universe, basically. I think Agent Carter is one of my current favorite examples. I mean, I guess it's an edge case because it's a show that is composed almost entirely of badass normals, but they're frequently up against superpowered people. I think that's the aspect of it that really gets to me so hard (and yes, Murphy in Dresden Files is another example I like) - it's partly that they're significantly underpowered compared to the people they have to fight, and partly that they're ordinary, so they have to make do with ingenuity, hand weapons, and non-combat skills (e.g. computer hacking) against enemies with magic, superpowers, etc.

For the latter reason I think characters like Vlad and Karkat don't quite hit that particular button for me because part of it is the ordinary-personness, almost self-inserty in that way, although I realize that is a bit of an individual quirk because this is a trope that I really like, so it's something I have specific preferences for. It's really more characters like Pepper in the Iron Man movies, or Peggy & co., who hit that button particularly hard. (I mean, in some sense I guess Iron Man is also a badass normal if you think about it, but doesn't really feel like it; he's not really presented that way.)