A sphere with initial charge of 8 microcoulombs touches three neutral identical spheres successively. What is the final charge on the initial sphere?

The initial sphere has a charge of $8 \mu C$. It makes contact with the first neutral sphere (charge $0 \mu C$). Since the spheres are identical, the total charge is distributed equally.
The charge on the initial sphere after the first contact is:

$$Q_{1} = \frac{8 \mu C + 0 \mu C}{2} = 4 \mu C$$

The initial sphere (now with $4 \mu C$) makes contact with the second neutral sphere (charge $0 \mu C$).
The charge on the initial sphere after the second contact is:

$$Q_{2} = \frac{4 \mu C + 0 \mu C}{2} = 2 \mu C$$

The initial sphere (now with $2 \mu C$) makes contact with the third neutral sphere (charge $0 \mu C$).
The charge on the initial sphere after the third contact is:

$$Q_{3} = \frac{2 \mu C + 0 \mu C}{2} = 1 \mu C$$

The final charge on the initial sphere is $1 \mu C$.

The correct option is a).

The final answer is $\boxed{\text{1 \mu C}}$.