Have come across some visually amazing time lapse videos yet noticed the camera moves in "real time".

How does one do that ?

My best guess is the camera is moved super slowly while in time lapse mode and when played back...voila !

You'll need a motion control dolly or slider, or a repurposed motorized telescope mount. There are plenty of forums available and pre-made products ranging from a few hundred to a few thousand dollars.

You might want to start your research here: Motion Control & Time Lapse Equipment Review | izmostock (http://www.izmostock.com/2011/03/motion-control-time-lapse-equipment-review/)

Many moves as Oren described, and they look great!

Another technique, which can look pretty good, depending, works when shooting timelapse with a dSLR. Since you've frequently dealing with an image sequence of greater than 5k resolution, you can zoom, pan, tilt, dutch roll, etc. in post. These don't quite look like their real-world counterparts, but can be very effective.

I've not gotten very far with this yet - initial testing showed that these image sequences are darn hard to preview, I've had to render to see results, which means planning the move blindly and very carefully!