The best approach in my opinion is pure stealth! Sure some missions force you to knockout guys. Although the obvious and easy choice is stealth. How much will you use? Will you sneak around and not get caught? Will you sneak around kill some, knockout some, and get caught? Will you just run around and slaughter any living thing? I personally prefer to not get caught, not kill, and not knockout(unless the mission says to do so). I have only gotten caught one so far but that was by The Golden Child and I had no Invisible potions and no way to get past him. I am curious to hear how you guys play.

I always prefer as stealthy as possible, using as few (hopefully none) of my supplies and no knockouts. Ghosting where I can.

The nice thing about Thief 1 and 2 is that in addition to the official difficutly levels you can set your own. The most extreme is "ghosting", where you are never seen by any NPC, and the only changes to the level when finished are those actually needed to finish the level.
A bit too extreme for me, but I know some of the more hard core taffers enjoy this challenge.

Agreed. Play the game the way you want to play it. It's a nice feature of Thief that it doesn't force you to play one way.

I agree - one of the things I love about Thief is that you are generally free to make your own rules as you go along. I personally like to knock everyone in the level out, I find it quite therapeutic to whack them all on the head with a blackjack and then hide the bodies :)