Electrical wizard I am not...but this has me stumped and maybe the answer is right in front of me but I can't make heads or tails of it.  If a series circuit has 3 resistors, and lets say resistor #2 fails, will the other 2 resistors continue to work?  Will the circuit continue to work?

No.  If the resistor fails, it will fail to an open condition, and you will no longer have a circuit, as there will no longer be any connection where the failed resistor used to provide one.

Mike

Resistors commonly fail open so the circuit no longer functions because it is not a closed circuit any more.

Under 'bad' conditions things can get dicey though.

Some resistors can fail and when the circuit opens the voltage applied is excessive.
They then proceed to arc over and make the initial failure a sometimes spectacular event and a break that can survive the open circuit voltage is established.