I tried reading in on this and was met with a ton of people talking about metalcore (which isn't metal), nu-metal (which also isn't metal), and bands I personally can't stand.
Now I will explain how they aren't metal: metalcore is just punk sped up with distorted guitars added. (Yes I understand some 'metalcore' doesn't fit that definition but pretty much 99% of it does, and yes I'm biased so that 99% might be wrong.) Nu-metal doesn't really play the same as metal. Its riffing is different entirely, it uses pretty much everything as a rhythm instrument, it's practically rap with electric guitars. It's all tripe marketed to younger kids whining about *feeeeelings* instead of doing something interesting, which makes me think of grunge before metal. I've heard people characterize it as having a base of hard rock and then fusing other stuff into it, but I don't have a wide musical palate so I couldn't say there.
Try giving this a read; http://metal-archives.com/ . Encyclopedia Metallum is a pretty good place to go for metal. I've found a number of interesting bands no one's ever heard of before thanks to it (off the top of my head, Kalijuge).
Kudos to the guy on the front page who namedropped The Absence.
Now, personal taste time! Doom is good, but I tend to prefer genre-bending doom that's mixed up with melodeath. Funeral doom is listenable but I generally save it for things like "I'm trying to sleep." Thrash is good but I don't like a lot of it for seemingly random reasons. Melodeath is great but I don't listen to much straight death (generally find it boring and when they go all gore-styled it's just ridiculous and childish). Tech death I find somewhat hard to listen to but when the mood strikes me, it's amazing. Prog is ok but I can't STAND Dream Theater and that's all any one seems to talk about when 'prog metal' is in question. Black I don't much like the sound of but I've heard a little done well.