I have 200 watt RMS speakers. Do I need a 200 watt amplifier to drive each one?

The best method when matching speakers to amplifiers is to use the "RMS" power ratings instead of "Max/Peak" power ratings.

It's important to note that most speaker manufactures publish two different power ratings:

Speaker "RMS" Power Rating
The "Nominal" or "RMS" (root-mean-square) rating is the amount of power that can be applied to the speaker under normal circumstances. One of the primary factors that determine the power rating of a speaker is the size of it's voice coil. A speaker with a high power rating uses a large voice coil, allowing more heat to be dissipated and therefore allows more power to be applied to the speaker.

Use this power rating to match the speaker's "RMS" capacity to an amplifier's "RMS" output. For example: if your speakers are rated to handle 50 watts RMS each, then select an amplifier that will deliver approximately 50 watts RMS to each speaker.

Speaker "Peak" Power Rating
The second is the "Max" or "Peak" rating which is the maximum amount of power that can be applied for short periods of time without causing damage. If the peak power rating is exceeded for an extended period of time, there is danger of overheating and deforming the voice coil.

***Do not use this power rating for matching speakers to amplifiers. It is for informational purposes only. Do not match the speaker's RMS power rating to an amplifier's Max/Peak power output. For example: If your speakers are rated to handle 50 Watts RMS each, and you select an amplifier that will deliver 125 watts RMS per speaker, you will likely apply too much power for the speaker to handle. This can cause a voice coil to literally "burn" and possibly "short-out," rendering it inoperable.***

In the question above "Do I need a 200 watt amplifier to drive a 200 watt speaker?" the answer is simply NO. A 200 watt RMS power rating is how much power a speaker can handle, not how much it requires. 

NOTICE:  Even a 200 watt speaker can sound great with only 10% (20 watts) power applied. However, you'll have low SPL (sound pressure level) or "loudness" with this little power.

Sample Amplifier Power Rating Chart:

Amplifier Power Low Side:
0.10 x (# of Speakers x RMS Power Rating = Required Amplifier Power)

Amplifier Power High Side:
# of Speakers x RMS Power Rating = Required Amplifier Power