To add to the discussion, I will share a short story:

I was out at the clubs last weekend, and i was just sort of cruising around and at one point just hanging at a table near the dance floor having a drink. I saw a girl not too far away dancing with some random guy - this she did not look all to pleased about. I smiled at her, gave her a joking thumbs up, and went back to my drink and conversation with friends. I didn't think much of it until i got the direct approach pulled on me: i was walking towards the bar for another drink when the girl's friend stopped me to tell me that the girl thought I was cute and wanted to talk to me. Herein lies the proof of the DA - hearing someone compliment you (in a flattering and honest way, not in a creepy i've-been-staring-at-you kind of way) makes you want to at least engage in a small amount of discussion with her.

So I went and talked to the girl for a little while, but found that there wasn't a major connection. Got the number, but decided that since she was leaving in 2 days for home (10 hours north) for the Christmas holidays I wouldn't pursue too much. Neither of us were looking for a one-night stand anyways. I texted her telling her it was wonderful to meet her and that maybe we'll run into each other in the new year.

The moral of the story is, really, that the direct approach can work if done properly.