Will restarting the computer a lot (about 10 times in 2 minutes) damage the motherboard?

Restarting your computer a lot shouldn't hurt anything. It could add wear-and-tear on components, but nothing significant. If you're completely powering off and on again, that'll wear things like your capacitors a bit faster, still nothing significant. The machine was meant to be turned off and on. And unless your machine was made from complete garbage, the added wear won't change it's performance until long after it's become your newest boat-anchor due to antiquity.

Now, if you're pulsing power off and on like 30 times a minute, that may have some implications. It'd really depend on the specific electrical characteristics of your power supply and motherboard.

This gives me an idea for a crazy hack-a-day project one could do - pulse a computer off and on at a fairly fast rate until it fails - just to see how long it takes..

It really shouldn't. The only thing that I could think of that could be harmful is that sometimes a reboot will cause a HDD to spin down and then power sent to the HDD. The constant powering down and powering up of the HDD is less than ideal. Also, CPU fans will sometime do a max spin up upon rebooting. Again, not horrible, but less than ideal.

I had a Windows XP computer that was stuck in a BSOD death loop with rebooting. It sat there for about 10 days constantly rebooting. I ended up formatting the drive and getting it running again. This was 4 years ago and it's still running strong.

That is not to say that you'll have bad luck one time and fry something...

Not really.

Leaning against the power cord on an older system connected to a faulty outlet can when it causes the power to flicker across the system several dozen times in a few seconds. That happening within the last week of the 1st semester of classes when I've got a boatload of English 1A papers to turn in is a quick way to learn about Data Recovery tools and OCR (scanning the old versions of the essays in to save retyping time).

But no, frequent reboots, as long as they are on purpose and not from bad power situations, will not generally cause problems.