Uh-oh, music industry guy is here to spoil the fun.
Lots of silly misconceptions in this thread including those held by the posters criticising the misconceptions.
Regarding metal, whether you are a fan or you hate the stuff with a passion, see the excellent documentary "Metal: A Headbanger's Journey" for a comprehensive overview of the style as a whole and a list of metal sub-genres.
Regarding whether [insert your most hated artist/style here] is music or not - of course it is. You might think it's BAD music, and that's completely fine, but to say that it ISN'T music at all is obviously incorrect in every single case to which it is applied, no exceptions. It's like saying that a cat isn't an animal because you don't like cats. Electronic dance music, techno, trance, etc: I think this is mainly by-numbers garbage for the uncritical and E-happy. It's still music though. Sure, I'd like to be able to say "that's not music" but I know, deep in my heart, that I'd be full of shit and just taking a cheap shot.
Regarding rap: rap = a vocal style. Hip-hop = an overall cultural movement which encompasess music (rap vocal style, turntabling, beatboxing) and other cultural aspects (fashion, graffiti art, breakdancing, etc). None of this stuff has anything to do with "gangsters" or "sex and drugs" by default, but (the better) rappers do tend to rap about what affects their community and lifestyle (although usually not them personally, or they'd be dead, in jail or the STD clinic). Is it any good? Well, that's highly subjective, isn't it. You might think it sucks but millions disagree because they buy it and apparently love it, so who is right and who is wrong?
Lady Gaga - I don't understand why she is so hated, in 2010 this baffles me. I guess it's kind of trendy to hate her at the moment but I don't see anything all that different about her which deserves hatred. So she dresses a bit funny - so fucking what, what pop star doesn't dress funny, people have been dressing weird in music ever since David Bowie donned a lady dress for the front cover of "The Man Who Sold The World" in 1970 (and probably before then, too). Dressing funny (or undressing funny) is a way to get people's attention, having great songs and being a great performer is then how you hold that attention. She's obviously extremely talented, other people have linked YouTube evidence in this thread so I won't. Sure she says a few outlandish things to the press sometimes and exhibits strange behaviour on occasion - so did just about every popular rock or pop artist you could name active from 1920 onwards. Lady Gaga has songs people like, and people buy them in their millions. No-one is forcing people to like these songs and to buy them. She makes pop music because it sells, and she wants to make it. People buy it because they want to hear it. If you don't like her music, don't hate her for it, that's just silly and a waste of your energy. Instead, just don't buy her music.
Punk - highly subjective term. No clear consensus has ever been made on what "punk" is, so it's fairly nigh-on impossible to determine if it has "died" or not. Some people say it died as far back as 1977, yet there are still thousands of "punk" bands active around the world, so either punk is what you make it, or someone has obviously slipped up somewhere.