$1990-1980+1970-1960+\cdots -20+10 =$
$\text{(A)}\ -990 \qquad \text{(B)}\ -10 \qquad \text{(C)}\ 990 \qquad \text{(D)}\ 1000 \qquad \text{(E)}\ 1990$
In the middle, we have $\cdots + 1010-1000+990 -\cdots$.
If we match up the back with the front, and then do the same for the rest, we get pairs with $2000$ and $-2000$, so these will cancel out.  In the middle, we have $2000-1000$ which doesn't cancel, but gives us $1000 \rightarrow \boxed{\text{D}}$.