I love the visual identity of steampunk. When it comes to looks, they are definitively a subculture of their own, but what about the music?
What do they listen to in addition to Abney Park?

Good question, I never thought about it...
I just assumed they listen to goth...

TO GOTH Young lady (I assume you are, compare to me) I must correct you.
Whole life Ive been tinkering with steampunk even before it became so popular. And when I get to my workshop I play mostly classical tracks or something more electronic thats popular.
On other hand I can understand you becouse there are some lost souls that love to dress up to steampunk and then behave like cybergoths. Not a clue whats wrong with them or this lame chick

Sir Ironlord, can you give us some more info? Maybe a list of bands or a playlist? That could be interesting...

Oh come on people! Steampunk is a sci-fi/fantasy genre, it has nothing to do with music and it sure as shit isn't a musically based subculture.
Asking what is steampunk music is like asking what is Star Trek music. Sure, you can have bands that are themed in that way but there is no distinguishable feature of their music that connects them into a distinct musical genre.
Hell, if you google steampunk bands one of the first hits you get is a list of steampunk bands where the following criteria determines whether you make it on the list:
1. They call themselves steampunk.
2. Old-fashioned dress or style (Victorian/Edwardian or 20's through 50's for dieselpunk).
3. Classical instrumentation elements.
4. Fictional (preferably alternate history) backstory.
5, Steampunk (sci-fi/historical) lyrics.

So basically, only one of the five factors has anything to do with music and even that is kept really vague (you can have classical instruments in anything from polka to metal) while the rest is just what I mentioned, thematically appropriate garb and lyrics.

Well, that is just like defining some weird genres of metal, doesn't make them any less weird or metal

Agreed. Metal genres can be like that also and I have a problem with that too! If your music sounds exactly like a more well established genre but because you have a thematic component to your lyrics or stage presence you invent a whole new genre to call yourself... I don't know, to me personally that is annoying.
In one sense you can call yourself whatever you want, who gives a shit, but on the other hand you are not doing yourself any favors because you are just muddying the waters and bringing more confusion to an already convoluted collection of genres and subgenres

Im also suspicious in art values and authenticity of Steampunk melodies. But then again aren't we all about something.

Suspicious. Please dont get me started

For Catwhisperer there is an answer which I found also. On the tip of browser, not further
I hope the list of artists will suffice

I wanted to agree with Ghazghkull right of the bat but figured I'd listen to this compilation first so it doesn't seem like I'm talking out of my ass.
First I want to say that I also think a musical genre should be a group of bands that share a similar sound or musical style, not just a theme or particular lyrics like some types of metal (I'm looking at you viking metal )
Having said that, with a few exceptions that sound like some electro crap, epic fantasy instrumentals like you would hear in an Elder Scrolls game or just plain rock 'n' roll, a bunch of song from this compilation do have a distinct sound I just wouldn't call it steampunk. It sounds more like carnival music.