jmc

Put the numbers in groups of $4$: $(1-2-3+4)+(5-6-7+8)+(9-10-11+12)+\cdots +(1993-1994-1995+1996)$ The first group has a sum of $0$. The second group increases the two positive numbers on the end by $1$, and decreases the two negative numbers in the middle by $1$. Thus, the second group also has a sum of $0$. Continuing the pattern, every group has a sum of $0$, and thus the entire sum is $0$, giving an answer of $\boxed{0}$.