I don't think Danger's plan works if you intentionally look for something else to find the original thing. I think that approach requires the original item be of no use, already replaced or redone, and the deadline long passed, then you'll find it sitting right out in the open where you know you looked a million times.
In the likely places for it, get a big box and take each and every item there and physically move it to the box. When the surface is empty, then put the stuff back (you'll have a really clean apartment when you're done too). I find I'll sometimes look all over my desk, think I've looked under every book and scrap of paper, etc., but there was just one piece of paper that never got moved and what I'm looking for is under that one.
If it's not there, check the less likely places. Near the coffee pot, inside the refrigerator, under the pile of dirty laundry, on top of the washing machine, get a flashlight to look behind things (I've done the "scour the car" thing before and still missed something that slipped between the center console and the passenger seat...can't quite reach down to feel with your hands and can't quite see clearly in that dark space). If your seat cushions are removable, remove them. Sofa cushions too.
Try to remember the last time you KNOW you had it. What were you doing that day, where did you go, what did you wear, what was the weather like (did you throw on a jacket you rarely wear because it was raining, or have a bag with you to carry your stuff in that you don't usually use in nicer weather).
Did you do any cleaning since you last remember having it? Maybe someone was coming over and you quickly tossed everything from the desk and floor into the closet or into a dresser drawer? Check the bottom of the closet and inside shoes...if it was in a jacket or pants pocket, it might have fallen out in the closet and landed in a pair of shoes...look in the pair of dress shoes you almost never wear since you'd have noticed by now if it was in the sneakers you wear often. Oh, and how about your gym bag? And call your gym's lost and found in case you had it and it fell out into one of their lockers. Same at the lab, check with your department secretary if anyone dropped it off as a found item, etc.
Good luck.
Edit: Oh, one other suggestion as a last resort -- find a nice woman, get married, then tell your new wife you lost it, and she'll roll her eyes at you as she points to it in plain view and tells you, "You'd lose your head too if it wasn't attached to your neck."
Dirty laundry, jackets, bags, taken by mistake by someone you know, a friend's car, a friend's house, a drawer, fell behind something...
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