Probably, Thermal shutdown of the LDO would worked.
See the Chart.
http://forum.rapiro.com/thread/255/
In this case(DC12V),LDO　can source 0.5A.

Solution 1. Use 6V 30W class AC-DC adapter.(But I can't find the adapter in Japan.)
Solution 2. Use 12Vto6V Step-down converter, between the 12V power supply and DC jack
Solution 3. Use 12Vto5V Step-down converter.(See the block diagram. My Rapiro is this Solution. https://github.com/oga00000001/RapiroTools/tree/master/PowerSupply

Please look for similar Step-Down DC/DC converter.
http://akizukidenshi.com/catalog/g/gK-07728/
http://akizukidenshi.com/catalog/g/gK-06969/
http://akizukidenshi.com/catalog/g/gK-05758/
http://www.aitendo.com/product/3851 (My Rapiro use this DC/DC)

So what you are saying is I put too much current load on the LDO and caused it to overheat? Because i was using 12V input vs 6V input?

I have a power supply that also has a USB out that I am using to power the raspberry pi. Should I remove the power pins coming from the rapiro board to the pi as well?

(It was working fine with those attached until i tried to connect the DC-DC converter to the I2C)

Also hello oga, I noticed you used my edits of the arduino firmware which were featured on the site for incorporating the distance sensor :D
As soon as I get my new rapiro board in, I'm gonna start working on auto walking and adding in object recognition...

I think the cause of fried.
1.Overload
2.Thermal shutdown of LDO worked
3.Current source stop from LDO
4.Revers current or Ground bounce from boost DCDC. (Effect of L (boost DCDC)) ?
5. Abnormal voltage generation.
6. Damage to other devices

Boost DCDC, I think it only increases the load current, that there is no effect on the stability operation.

If you need power, I recommend that you use the other step-down converter.

http://www.dx.com/p/mini-dc-dc-step-down-adjustable-voltage-regulator-166930#.U2w_V6h_uSo