Which alkyl bromide reacts fastest with $\mathrm{NaI}$ in dry acetone (SN2 conditions)?

SN2 needs backside attack, so steric crowding at the carbon bearing the halogen slows it. The unbranched primary bromide is least hindered, while the secondary and tertiary bromides are more crowded and the neopentyl bromide is blocked by the adjacent quaternary carbon. Hence $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{CH}{}_2\mathrm{Br}$ is fastest.