There are really two independent issues here that you have to address separately.
An arduino output pin always needs external protection from trying to draw too much current from the output pin. A 8 ohm speaker (of any wattage rating) will draw too much current if directly wired to a arduino output pin. Adding a series resistor between the output pin and the speaker will protect the output pin, and 150 to 200 ohm resistor is a good choice. However this resistor will severely waste most of the 'audio power' and prevent the speaker from having very much volume at all.
A speakers 'wattage rating' is it's maximum power handling ability, sort of how high a volume it can attain before distortion sets in or it burns up. To drive most any speaker to whatever maximum value it can handle requires a audio amplifier rated at near the same value of the speaker. But keep in mind that people run their amplifiers and speakers using a volume control to the volume level they are comfortable at listening to. I have a vintage 70s hi-fi system where the amplifier is rated at 250 watts RMS maximum output per channel and I'm driving two large 12" 3 way vintage speakers rated at 50 watts handling power. I can fill my room will very loud music where the amplifier is supplying around 2 watts of average output.
So keep in mind what you are trying to attain and that any speaker sound you wish to generate from an arduino project will require at least a small audio amplifier, one or two watt amplifiers will work just fine with nearly any speaker rated at 8 ohms.