That first Regexp will fart. See, the way it's written, it will match either a 'y' at the beginning of the string, a 'yes' or 'n' anywhere in the string, or a 'no' at the end. You need to put parens around the patterns to isolate them from the anchors. Also, I'd prefer an elsif to nested ifs:

if (/^(y|yes)$/i)
    {
        print "YIPPEEE.!!!!\n";
    }
elsif (/^(n|no)$/i) 
    { 
        print "Begone, evil peon!\n"
    } 
else 
    {
    # Validate user input and return message if invalid
    print "\n\n=====================================\n";
    print "You Have Entered and Incorrect Option\n";
    print "Valid Options are [Y/N]\n";
    print "=====================================\n\n";
    &answer;
    }
[download]

However, I would much prefer to use a for as a switch case:

SWITCH: for ($input) {
    /^(y|yes)$/i && do {
        print "YIPPEEE.!!!!\n";
        last SWITCH;
        };
    /^(n|no)$/i && do {
        print "Begone, evil peon!\n";
        last SWITCH;
        };
    # Validate user input and return message if invalid
    print "\n\n=====================================\n";
    print "You Have Entered an Incorrect Option\n";
    print "Valid Options are [Y/N]\n";
    print "=====================================\n\n";
    &answer;
}
[download]

LAI
:eof