Don't forget that our friend next will work in a while loop. Combining some of these answers gets you the technique I prefer:

while (<FILE>) {
    next if /^#/;    # skip lines starting with comments
    next unless /\S/;
    # do something with a real line here
}
[download]

This allows you to use a normal loop construct (makes sense to me) and short-circuit it at the beginning if certain conditions are met. It makes cleaner code than a lot of if-elsif statements.