Almost always request the voucher, not the free ticket.

Reasons:
Free ticket usually does not earn miles.
It is usually taken from award availability so there may be restriction on dates it can be used.
You can most of the time find fares from A to B in the domestic US for $300 or less. (which I believe it the normal domestic $ voucher amount... well at least it is for Northwest).

With a voucher (ECV) you can use all or part of it.
It can be applied to a higher fare (more then the voucher is worth) and it just acts like a money off coupon.
You earn miles.

Since I am most familiar with NW that is what I use as a reference. It may be different for other airlines.

Other things I do... when arriving at the gate I ask them if the flight is going to be full or overbooked and then say that I am willing to be bumped.
I don't even bother to check how full the flight is anymore. Of course, if the gate area is empty and it is 10 minutes to boarding I don't ask.
Stay near the gate (GAs), but do not hover.
As mentioned previously as soon as you hear something like they are going to ask for volunteers, get to the desk.

I've had several bumps both by myself as well as when traveling with my family. If I remember correctly my family of 4 received a bump on a flight I was paying for with a voucher (I'll have to check my records to be sure) that I had earned while traveling on my own. If it was the same time I remember we ended up arriving only 45 minutes after our original flight had landed but we ended up flying to a more convenient airport that was only 15 minutes away from our destination as opposed to 45 min.
I had suggested the alt airport to the GA and knew there was space on that flight. She was actually excited that I had a plan.

Currently, I have a $300 ECV burning a hole in my pocket from a bump that got me an extra connection and a visit to an airport that I hadn't been to for about 15 years.

Where to go, where to go?