8Ω speaker, what resistor values to use?
The speaker rating of 8&nbsp;&Omega; is AC resistance, speaker impedance. Impedance (AC-Resistance) changes based on the frequency of the signal fed into it.  

If you are worried about hurting the speaker and need to calculate power driving that particular "load", look at the speaker Wattage rating. 
Say it is 1&nbsp;W for example, and you are providing 5&nbsp;V d.c., the amperage required will be: 0.2&nbsp;A.

V * A = W 
0.2 * 5 = 1


So the DC resistance is actually: 

V = I * R (0.2 / 5 = 0.04 Ω). 


Give it a higher amplitude... say 5.7&nbsp;V to account for a transistor no resistor, and you get about 0.175&nbsp;A. and a change in DC resistance again to 0.0301&nbsp;&Omega;.

If the power supply is AC, the impedance needs to be matched to the speaker impedance to get best energy efficiency, otherwise the amplifier can be damaged.  

For that circuit I suggest you place a variable resistor where the resistor is in your circuit to allow for a volume change. Also a flyback diode maybe a good idea, that will protect the speaker but take down voltage 0.7&nbsp;V d.c. keep in mind you have that transistor there adding 0.7&nbsp;V d.c.! so it evens things out too using that diode.

That diode placed on the high (+) side of the circuit, before the speaker and after the variable resistor.