$1-2-3+4+5-6-7+8+9-10-11+\cdots + 1992+1993-1994-1995+1996=$
$\text{(A)}\ -998 \qquad \text{(B)}\ -1 \qquad \text{(C)}\ 0 \qquad \text{(D)}\ 1 \qquad \text{(E)}\ 998$
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 $\boxed{C}$.