Ok, here are my interpretations:
FOR MY DEMONS - Pretty much like a lot of other people said: something really bad happened to the singer, and he's haunted by it. Not only that, but he somehow knows that whatever it was is coming back around. It kind of sounds like he's angry at the person he's singing to, as well. I guess he/she had something to do with it. 'My problem was that you kept me here too long/And today is when we'll regret that I came by.' The impression I get is that something bad happened to him at this place he used to live, and he left but then returned, and realized he shouldn't have come back, but somebody kept him too long and something ELSE bad happened. Heck, I don't know. Those are my guesses.
WE MUST BURY YOU - I take this whole song literally. He and some other people murdered somebody, and now he regrets it and is asking the deceased's forgiveness.
DISPOSSESSION - Betrayal. Someone fucked him over, and now he's depressed and pissed. I interpret it as being about a failed relationship, but one that failed more because of the other person than because of mutual incompatability. Like I said, betrayal. I love this song.
WILL I ARRIVE - All of 'Viva Emptiness' sounds like a mafia movie to me, lyrically. I realize it's not a concept album, but it feels like one to me, with common themes of crime, betrayal, and general urban bleakness running throughout. This song just sounds like one part of the story, wherein he's taken back to an old neighborhood by a gang (maybe) that he's fallen in with, but everything looks different and wrong. During the chorus, I get the impression that he was sort of coerced into joining these people, maybe by someone he loves. But because of the line, 'I think about what you told me/When I was about to join in', it sounds a little like he was going to join anyway. Not too sure. Either way, 'Look at me now/They have cut my hair/It's a long way back/They kicked me down/And I could not rise/I will never arrive' implies to me that he regrets his decision to join, and fears that he won't be able to go back to what he used to be.
SULFUR - I think EternityRites nailed this one. Good job! I never even thought about the end of a match. Great, great lyrics in the last part of this song.
BURN THE REMEMBRANCE - Pretty straightforward: he's speaking to someone (or imagining that he is) that he used to be in a relationship with, which ended. A basic and very effective (and affecting) lamentation of what was lost, especially, 'But you were standing against the hotel wall/Frozen in an unknown thought' -- same meaning, I think, as in the song 'Gone': 'You were already thinking of going away.'
IN THE WHITE - The lyrics on this album are kind of obscure to me, even though I still relate to them very much. It sounds like it's about getting over something, and lamenting that some other person doesn't see in you what you see in him/her, until it's too late. 'And if you don't see, I'll remain unseen/Until there's time to be remembered.'
EVIDENCE - A couple have to infiltrate some place. Before they start, the 'main character' is telling his partner/lover (I prefer the latter) that everything's going to go fine, even if they get separated. But, of course, the mission goes awry and he's captured by Them (not the King Diamond 'Them'). They also catch his partner, but apparently she sold out to them, and by proxy betrayed him, so they let her go, or at least didn't punish her. But he's going to be detained indefinitely. He gets to speak to her one last time before she goes. Part of him is glad that she gets to go free, but another part of him is angry at her betrayal. 'You passed the test and that's so good for you.' Very biting remark, but not entirely sarcastic. He still loves her, and tells her he's going to write to her, although I get the feeling that he doubts she'll read his letters. I get the picture of a guy sitting behind glass with his hand on the window, watching as she walks away, never to be seen by him again. This song is very moving to me, and definitely one of the best they've ever done.
UNFURL - Again with the urban/mafia themes, I think. He's supposed to meet someone 'at city's center'. He's spoken to him/her (I think 'her') on the phone, and he's been told that he has to choose whose side he's on. In the chorus, it sounds like he's just having a smoke and remembering back to younger, less troubled times. By far one of my favorite Katatonia songs.
Hope someone got something from this. Needless to say, I'm no more qualified to interpret Katatonia songs than anyone else here (except Jonas and probably Anders), but being that I love this band and have always related very strongly to their music/lyrics, I thought I'd have a crack at it anyway.
Skål!