Also it's usually a good idea to add double quotes around the values; you will get very confusing error messages if either of the variables would turn out to contain an empty string (or a vast array of other possible problematic values).

Code:

if [ "$VAR1" = "$VAR2" ]

In real-world scripts, you frequently see a leading X added to the values, to guard against some of the remaining problematic scenarios (if $VAR1 has a value containing a dash as the first character, for example).

Code:

if [ X"$VAR1" = X"$VAR2" ]

For these reasons, I personally tend to recommend case over if for string comparisons.