Everybody defines "goth music" in a different way, but I can recommend you what I like: if you are into bands, try Epica, The Gathering, Within Temptation, After Forever, Lacuna Coil, Nightwish, Lacrimosa, Evanescence (to name a few that are well known). Less known, Sirenia, Tristania, Lullacry, Therion, Xandria. If you are more into ambiance music, my favorites are Nox Arcana and Midnight Syndicate. And of course, if you like Nature Sounds, a CD with thunderstorms and rain is perfect. I'm afraid I don't know any club music.
Just my two cents. Good luck with your search!

indeed. what kind of music do you prefer? Since you like celtic, you might like more of the darkwave stuff (there's another term I'm looking for, neo-folk, I think, but I'm really sick and the little gray cells aren't working)

Check out this list of what DJ Merrick plays at Death Guild (she's listed under Upstairs. Scroll down) www.darkdb.com/deathguild/DateList.aspx

Of that genre, I rather like Qntal, Faith and the Muse, Cocteau Twins, Switchblade Symphony, Die Form, Miranda Sex Garden (the goth-rock branch of Medieval Baebes), Conjure One (ok, not exactly darkwave, more like goth-alternative), The Changelings, The New York Room, Claire Voyant, Dead Can Dance...

Awesome, I'll be sure to check into these bands.
Thanks for the suggestions!

Alternative, Celtic and weird? Try Faith and the Muse, Cocteau Twins, Cinema Strange, Current 93, Inkubus Sukkubus, maybe some Libitina, Death in June, and possibly Nick Cave (not celtic, but certainly alt and strange).
These should be a good intro to Goth for you, all having folky/celtic influences to a greater or lesser extent. If you want to try old school Trad Goth, get some Siouxie and the Banshees, Bauhaus, Cure, Sisters of Mercy, Mission, Creatures, All About Eve, Alien Sex Fiend (warning- ASF make some really strange sounds).
Then go and have a look through the goth music sites- just google 'goth music list' and you should get something- and you can get yourself many new bands similar to the ones you like. Pandora Internet Radio's pretty good for that, too.

I on the other had, have a far spread music collection - I'm all over the map musically.

Lately though (past month or two?), I seem to have developed a Gothic bent to my listening habits - which I think I'll say Evanescence got me started on this.

Stuff I like so far (thank goodness for eMusic):

New Skin
Switchblade Symphony
Anna Oxygen
The Shroud
Beat Mistress
The Shadow Dance
Die Laughing
Poe (ish)
Trance the Sun
Immortalis Amor
Sister Machine Gun
Dragon Style
Tapping the Vein (great version of Tori Amos' Cornflake Girl)
And of course, the Cure - Love Song - which I really didn't care for when it first came out (I think I was still in my metal phase then), is now a favorite.

I'm constantly on the lookout for more... but I find that just *finding* new Goth music can be hard - especially when you are new the genre and don't know all the good stuff. A few of the bands were more death-metal, which sounded more like noise (to me) than what I associate with "Gothic".

I'll certainly keep an eye on this thread and if someone wants, I'll try to toss together my collection thus far.

Then there is the whole question:

How do you define Gothic music?