Do you ever check out guys noticeably, on purpose? Why?

A few things that have happened to me:

• a girl will quickly and fleetingly glance at me a few times (the double-take)

• give me an up-down (the vertical-pan)

• and on the rare occasion stare for a few seconds (the stare-for-a-few-seconds).

I find it flattering, but it becomes uncomfortable because I never know how to respond to it.

Either I pretend like I didn't notice or I just smile back sheepishly.

I HAVE never, ever acted on it. (Read: approach the girl, and stir up a conversation) Partly because it's always when I'm walking around doing something, or trying to be timely for a meeting/prior engagement, but it is also because it's kinda awkward, and I'm a bit shy.

TL;DR: Yes or No? Why?