I think it's too broad a topic to give an all encapsulating answer to. So I'll break it down in a different way...
1) I don't finish most of the games I play (in fact, I've seen a recent gbatemp thread somewhere discussing exactly that, so I'm not alone)
2) of the finished games, I usually have a feeling of completion (this is what I set out to do, so I'm done with this
). If I don't, I don't see any reason to keep playing (I'm sorry for mass effect 3 fans, but I honestly don't get their reaction: "boooh...I don't like the ending. Oh, wait...lemme purchase a "better ending DLC").
3) there are only a few games where I still want to play the game after finishing it, and where simply hitting "start new game" won't work.
4) the DLC has to be quality as well, and fit my tastes (sorry, but map packs and/or some skins don't matter to me).
If any of those conditions isn't met...then yes, I'm indifferent towards DLC. But in those rare games (I've finished it, loved the ending, want to play more AND where the DLC is quality)...then sure: I'm all for it.
Gamers who played nineties games probably know what I'm talking about: it's just called "an expansion". That you download this from the internet changes the name (yes, it is DownLoadable Content) doesn't change that experience.
Let's get the obvious ones I like out of the way first: red alert 2: Yuri's revenge and the 2 "other" campaigns of starcraft 2 (though even by these standards it's hard to say as they are standalones now as well, iirc
).This sort of grandiose "more game" is always welcome. I assume this goes for most of us.
Then there is the sort of "small expansion" that is harder to quantify. As a virtual board game player, I get to see many of these: these (usually mobile) games first sell you the base game, and the DLC is exactly the same as the board game expansion. And my reasoning is there as well. Carcassonne has had many extra "tiles" in board game form (I don't even dare count them...It's in the dozens). So of course most - or all? - are available as DLC as well. I'm not always a fan of buying everything, but I certainly love that it's available. And for the few games I absolutely adore (ahem: race for the galaxy), I'd pay it twice over if I had to.
The last is akin to the 'skins and levels'. This is a relatively unique one, but I paid the most money on rocksmith 2014. What can I say? Of course I rarely spend an entire evening playing one song (let alone practicing a part of one), but I have bought quite a few extra songs over time. It's cheap and I can easily get my mileage out of it.