p/s/a: Going up to a girl pretty much anywhere in public and saying something like "I thought you looked cute and wanted to meet you" actually works if your body language is in order.
Is this true? Aside from the fact that getting "your body language in order" is easier said than done, it would be pretty easy to do an experiment to test this hypothesis. You could approach one hundred women in this way and see how many responses you got of each of the following nature: active hostility, passive "please go away" politeness, friendliness, perceived actual sexual desire. You could even get, say, five different men from different quintiles of physical attractiveness to see how it varies.
I kind of want to do it myself, but to be honest I'm probably too much of a wimp.
If this seems too scary, going on Chatroulette or Omegle and being vaguely interesting also works, and I know people who have gotten married from meeting this way.
The one time I went on Omegle everyone kept next-ing me almost instantly, and maybe one out of five times they next-ed me as soon as I said "hello" or the equivalent. I can't think of any characteristic I have that would make me exceptionally next-able, so I concluded that Omegle was a really frustrating waste of time. I'm confused as to why other people concluded otherwise.
I've not tried it myself(at least, not often enough to have useful data), but from all I've heard it can work. It's low probability - single-digit percentages for most guys, it seems - but the investment of time and effort in doing it is sufficiently low that it can still be a good strategy, as long as you have a high tolerance for rejection.
P/S/A: There are single sentences which can create life-changing amounts of difference.