Proton affinity is a measure of the basic strength of a species. A stronger base has a higher tendency to accept a proton (higher proton affinity). According to the Brønsted-Lowry concept, a weak acid has a strong conjugate base and vice versa. The conjugate acids of the given species are $H_2S$, $NH_3$, $HF$, and $HI$. The order of their acidic strength is $NH_3 < H_2S < HF < HI$. Since $NH_3$ is the weakest acid among them, its conjugate base, the amide ion ($NH_2^-$), is the strongest base. Therefore, $NH_2^-$ has the greatest proton affinity.