I'm really into black metal more than anything else. Amongst my favourite bands are Taake (pronounced "toh-keh"), 1349 and Carpathian Forest but I'm into a lot of other black metal bands. I'm quite into the DSBM sub-genre (DSBM stands for depressive/suicidal black metal, but I listen to it for the atmosphere and raw emotion, not because I'm depressed or suicidal). I would say Woods of Desolation and Coldworld were my favourite DSBM bands. Also, though they're not DSBM, the band Lifelover was similar and I like them a lot (I don't really know what
to classify them as). For intro to black metal, you definitely shouldn't start with DSBM or bands like Taake. Although I hate the album, the best way to start would probably be Satyricon's album The Pentegram Burns (specifically the song KING). I hate it because it has a very radio friendly sound (for black metal) and I see it as a betrayal to the genre, and the fact that it comes from one of the very best black metal bands rubs salt in the wound, but I think it's more palatable to someone who hasn't acquired a taste for black metal. The later albums of the band Mayhem are similar; the only song from their later albums that I like is called Dark Night of the Soul, so you can start with that one.
Other essential black metal bands are
* Bathory - Swedish progenitor, basically defined the low production value and raspy vocal style that would prevail in black metal. Later also invented Viking metal. My favourite song is called The Return of the Darkness and Evil.
* Burzum - another one-man project and probably the most infamous black metal act after he was convicted of the murder of Mayhem's original guitarist and the highly publicised arson of several Norwegian churches. My favourite song is called Belus' Død from one of his more recent albums.
* Darkthrone - only released three good albums (called the Unholy Trinity), though they were three of the best black metal albums ever released, and later turned into an insufferably pretentious punk band. My favourite song is Transilvanian Hunger.
* Gorgoroth - who have the most classic black metal sound as well as having probably the only seriously hardcore satanist band member in the entire genre. My favourite song is Open the Gates.
* Immortal - their later albums are also probably more palatable to someone unfamiliar with the black metal aesthetic, but without compromising on "trueness". Immortal also win big points for the frontman's personality. The thing to remember about Immortal is that they are basically a parody of the genre, despite having been at its forefront for their (and its) entire history. My favourite song is called Tyrants.
there are a lot more but I don't want to keep on about something that most people won't care about. If anyone does
care for more suggestions I can make them though. Also, check out this site: http://www.bestblackmetalalbums.com/top_100_black_metal_albums.php?&smode=100
it's actually a really good list and includes a few more obscure bands if you like to pretend to be really deep and all about the underground, like I pretend to be.
I also like death metal, generally the more technical side like Obscura, Necrophagist, The Faceless and later Death albums, but I haven't listened to much in a long while. If you're looking to get into death metal, you should probably start with Cannibal Corpse. I did. They're kind of the absolute standard death metal band so they're a good starting point. I think the first Cannibal Corpse album I listened to was Bloodthirst. Probably my favourite song from that album is Unleashing the Bloodthirsty so start with that.
Another of my favourite bands is Opeth although I've scarcely listened to or enjoyed anything post-2001 by them due to their gradual change from what was a complex fusion of black metal, death metal and avant garde/progressive metal to what is basically now progressive soft rock.
As for thrash, I never really got into it. I was very much into Megadeth, Slayer and old Metallica, and I'm aware of German thrash bands like Kreator plus a few other American ones like Exodus as well as Sepultura from Brazil (their first three albums anyway) but I don't really like any of those bands or listen to them these days.
Then there's classic heavy metal bands like Dio, Maiden, Sabbath, Priest, etc. who I do like, but again I never got really into them.
Finally, there's what I call operatic thrash metal to describe the bands Mercyful Fate and King Diamond (King Diamond being the solo project of the vocalist of Mercyful Fate), who I do quite like, though his vocal style really is an acquired taste. I recommend the songs The Candle and Corpse Without Soul by King Diamond (they are actually Mercyful Fate covers but I prefer the King Diamond versions), but again, the vocals will probably be an obstacle to most people at first.