First off, always use strictures (use strict; use warnings;).

The major problem is that the questions are embedded in the code. That makes the code incredibly fragile and horrific to maintain. Move your questions out into a data structure, or better still a file (then build the data structure). Consider:

use strict;
use warnings;

#variable initialization

my @questions    = (
    {question => "Question #1: Who is buried in Grant's tomb?",
     answers => [
        "Grant",
        "Lincoln",
        "Frank",
        "None of the above.",
        ],
     answer => 'a',
    },
    );
my $wrong_count = 0;


for my $question (@questions) {
    printQuestion ($question);
    print "\nThe answer is: ";
    
    $question->{reply} = lc <STDIN>;
    chomp $question->{reply};
    
    if ($question->{reply} eq $question->{answer}) {
        print "Correct\n\n";
        next;
    }
    
    ++$wrong_count;
}

print "\n\n";

exit if ! $wrong_count;

print "Correct answers:\n\n";

for my $question (@questions) {
    my $reply = ord ($question->{reply}) - ord ('a');
    my $ans = ord ($question->{answer}) - ord ('a');
    
    next if $reply == $ans;
    printQuestion ($question);
    print "\nThe answer is: $question->{answers}[$ans]\n";
    
    if ($reply > @{$question->{answers}}) {
        print "You didn't give a valid answer\n"
    } else {
        print "Your answer was: $question->{answers}[$reply]\n";
    }
    
    print "\n";
}


sub printQuestion {
    my ($question) = @_;
    my $letter = 'A';
    
    print "$question->{question}\n";
    for my $answer (@{$question->{answers}}) {
        print "$letter: $answer\n";
        ++$letter;
    }
    
}
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