When should I use UNSIGNED and SIGNED INT in MySQL?

UNSIGNED only stores positive numbers (or zero). On the other hand, signed can store negative numbers (i.e., may have a negative sign).

Here's a table of the ranges of values each INTEGER type can store:

^{Source: http://dev.mysql.com/doc/refman/5.6/en/integer-types.html}

UNSIGNED ranges from 0 to n, while signed ranges from about -n/2 to n/2.

In this case, you have an AUTO_INCREMENT ID column, so you would not have negatives. Thus, use UNSIGNED. If you do not use UNSIGNED for the AUTO_INCREMENT column, your maximum possible value will be half as high (and the negative half of the value range would go unused).

Use UNSIGNED for non-negative integers.

Basically with UNSIGNED, you're giving yourself twice as much space for the integer since you explicitly specify you don't need negative numbers (usually because values you store will never be negative).