Well, the specifically gothic bands that I used to listen to were:
Sisters Of Mercy (my favourite)
Bauhaus (listen to Crowds - seriously)
Dead Can Dance (I think of this more as world music, though it was recommended to me as gothic, and others in this thread have mentioned them)
I tried getting my hands on some CDs by Siouxsie And The Banshees, Fields Of The Nephilim and Alien Sex Fiend, but could never track them down. Those ones were recommended to me by various gothic websites. There was also David Bowie, but I think that is somewhat on the fringes of gothic. *shameface* I'm not actually that familiar with Bowie. *shameface* The ones listed in this paragraph are ones that I've not really heard a lot of.
The only traditionally gothic bands I've ever owned CDs for were Sisters, Bauhaus, DCD, as listed at the top.
Umm, I can list 2 metal bands that are oftentimes referred to as goth metal. Cradle Of Filth (lots of metalness, certain parts leaning towards gothdom) and Chalice (a band from where I live, who have since broken up, who are sometimes labelled Doom Metal, but I think the musical quality makes them more goth than anything else).
Then there's also Evanescence, as someone mentioned. I think that's somewhat in a category of its own. Eva has metal sensibilities, pop hits, and gothic style - at least most of the time it does, in my opinion.
I love Evanescence, but I find it hard to categorise them.
And if all else fails - search youtube. Just type in "goth band" or "gothic metal" or "doom metal" or whatnot, and hopefully you'll find something that suits your tastes.
1 I know I found by searching youtube was Epica. They're listed as metal, but the voice is all clean vocals. I was just mentioning this in case anybody out there thought that perhaps metal bands had to have the growl vocals. *shameface again* I used to think that. *shameface*
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If you take nothing else from this list, please listen to the song Crowds by Bauhaus. Or Marian by Sisters Of Mercy! Those songs are just awesome beyond words.