The speaker has that 1.5W, 8 ohms rating.
P = I*V, V = I*R, and so P = V[sup]2[/sup]/R or...
1.5 = V[sup]2[/sup]/8
12 = V[sup]2[/sup]
3.5 = V (approximately.)
So you don't need more than 3.5V to drive the speaker. 110V would make sparks and let the magic smoke out.
On the other hand, back to P=I*V, or 1.5 = I * 3.5 gives us
I = 1.5/3.5 = 0.43A, more than 10 times the current output of the Arduino. That's why you need the resistor as well.
With an appropriate limit of 40mA, you'd get P = I^2R or about 0.01W... (additional power dissipated in the resistors.)
You could get some louder by connecting multiple pins to multiple resistors before connecting the speaker, adding their total current capability.
Cheap powered speakers are so common and cheap these days that they're probably a better route.