What is the value of $1 - 2 + 3 - 4 + \cdots + 99 - 100$?

Group in pairs: $(1 - 2) + (3 - 4) + \cdots + (99 - 100)$. Each pair gives $-1$ and there are $\frac{100}{2} = 50$ pairs, so the sum is $-50$.