How many conditions in an "if clause" is acceptable?
You could put all of your variable names into an array and loop over it, something like this (pseudocode):

var names = { 'First', 'Second', 'Third' };

for (var name in names) {
    if (Request[names[name]] == null) {
        throw new ApplicationException('Error');
    }
}

// No errors if we reach here