I'm a huge fan of using music from other games. I like the MGS1 Alert theme for danger rooms and the MGS1Mantis' Hymn for FSC. The Monster Hunter 1 Desert fight theme fits for pretty much anywhere there's fighting.

I'm on my phone, so no YT links yet. I'll add them later.

Also, here are the obligatory Pokemon RBY battle theme and Guile Theme mentions.

"I like the MGS1 Alert theme for danger rooms"

I read that as Metal Gear Alert Theme - http://www.youtube.com/watch?v=ABuvCFLBnow

Best with gun puppy danger room.

I wish the boss fights were intense enough for music though. Sadly, they need some work. I really wouldn't mind having an excuse to listen to - http://www.youtube.com/watch?v=B_MW65XxS7s

Starting off, I have to second pretty much everything mentioned so far, except maybe One-Winged Angel. But that's a discussion for another time.

Starting in the "classic" vein, Cave Story. There is a nice variety of tracks here that all fit quite well with SK's feel. And it's freely available.
(Also, if you like Metriodvania/2d action platformers, do yourself a favor and click the download game link on that page. I'll wait.)

(Seriously, do it now.)

While extermely short, Blaster Master has some nice adventuring tunes in it. Jelly Helm is optional.

Next, there's Secret of Mana. Great Action-RPG, Best Boss Music. This on loop is required for at least run through of Jigsaw Valley/Aurora Isles.

Moving into (slightly) newer, There's Ragnarok Online. Lots of variation, good for normal areas but lacking in high-energy songs. Last I checked the game installed with a set of nicely tagged mp3s in a folder labeled as such.

Continuing down the list, there's Phantom Brave. Good pseudo-orchestral, heavy on the strings.

Parasite Eve is a good mid-range soundtrack with a more eletronic fell to it. A little bit for action, a good bit for exploration, a whole lot of reused motifs, but overall pretty good stuff.

Breaking away from all the RPGs, Einhander brings some good percussion for your diving pleasure. Switches between methodical beats and high speed regularly.

From planes to giant robots, the Armored Core series on the whole has some amazing tracks. In particular, the For Answer soundtrack has a strong set of battle tracks, and a few for when you are surrounded by just heat and crowns.
(I'd be doing a disservice to you all to bring up AC and not mention this. Link.

Dark Side of Phobos - Another great set of remixes, from Doom this time, for when you want something heavier. Link.)

And specifically for Candlelight Keep and those Graveyards, a little bit of Silent Hill. The soundtracks for 1-3 are among my favorites of all time. The original is mostly ambient, 2 tends towards eletronic drone, and 3 is more "normal." Also has some of the most terrifing boss music anywhere, but I"ll leave you to decide why.
Shadows of the Damned is quite similar, but with more action mixed in.

...That's probably good for now.

I was gonna suggest Cave Story but Lostillusion beat me to it. There's another freeware game called Vega Strike, which has a lot of variety in its music. IMO it's worth the download just for that. If you're interested in a 3D flight game with missions ranging all the way from freight hauling to PMC combat stuff, then the game is probably worth looking at too. :D

Vega Strike website at: http://vegastrike.sourceforge.net/getfiles/

I think the Party Button fight music is too in-your-face and clashes hard with the ambient music in most levels, and also gets repetitive since those fights are all over the clockworks. If Three Rings would just replace that with the upbeat variants that already play in other parts of the level, and use the existing music much less often and somewhere it clashes less, the music would be perfect IMO. Sustaining high-intensity musical dramaticity just doesn't work, but slightly uptempo ambient music is much harder to overuse. I like the music that plays in Cravat Hall in particular, it makes me want to dance or something, but I'd also like battle music with a taste kinda like what plays here.

Deadly Premonition has some good stuff in it, I really need to get around to playing it soon, but is when is it NOT time for sexy saxophone?

@Starinvf
I have done my job.

Wow buddy, don't hate on one-winged angel. You know you love it deep down.

Yes to Cave Story though. Also, if you're looking for some other music, consider the mega man series.

I play with the sound off. Nothing but a creaking keyboard and the occasional curse word.

...but since this is a suggestion thread and I'm a contrarion I'll suggest Modest Mouse.

http://www.youtube.com/watch?v=xa9YnCQIgDY&feature=channel_video_title - Lock's Quest Battle Theme.

http://www.youtube.com/watch?v=q0WignfItmg&feature=channel_video_title - Danger.

http://www.youtube.com/watch?v=mawWW4MN9UI&feature=related - Mario and Luigi Final Battle Theme RPG 3.

http://www.youtube.com/watch?v=rALUkPyYD24&feature=related - Mario and Luige Final Battle Theme RPG 2.

i'm obsessed with this song,please try it :D http://www.youtube.com/watch?v=my_W9ZHIUFI

Another one to add to my list:

Monster Hunter Freedom Unite - Nargacuga Theme (Snarbolax fight, since they're pretty much the same monster and all)

Ok, sorry, no Bastion tracks in the post below...

Try listening to Grand Theft Auto's radio stations... my favorites are Flash FM, Chatterbox and Vice City Public Radio...

If I had a choice, I'd replace music from all levels with the Aurora Isles background music, including boss fights.