Currently I am building a quadcopter with Raspberry Pi and I have four 20A Tunigy Electronic Speed Controller (ESC). I was wondering about could I use ESC's red wire to power my Raspberry-Pi? (tying 4 red wire out of ESC could fill the current requirement?).
It seems that you should be very careful using the BEC (Battery Eliminator Circuit) on your ESC. The hobbyking link says it outputs 5.5V while here it seems that the raspberry is very very picky at input voltages.
In my opinion 5.5V would be no harm at all but the specs were written by an engineer and it's better to trust them (on average). You can either search for better specs (these FAQs are not a specification) hoping for the best, try your luck hooking the BEC and the raspi together or search for a LDO regulator such as this, that seems to be in the 450mV range of dropout voltage sourcing 1A@5V. Keep in mind that 500mV is a very, very low headroom to put a regulator in between, but searching makes miracles sometimes.
I'd go for the last option, you want a nice 'n stable supply for the raspi anyway, and with 1$ you get the regulator and the necessary capacitors.