Personally, I'd read everything into a hash.

use Data::Dumper;

my (%quiz, $number);
while (<DATA>){
    chomp;
    if (s/^(\d+)\. *//) {
        $number = $1;
        $quiz{$number}{question} = $_;
    }
    elsif (s/^([A-Z])\. *//) {
        my $option = $1;
        $quiz{$number}{answer} = $option if s/ *\*$//;
        $quiz{$number}{$option} = $_;
    }
    else {
        next;
    }
}

print Dumper \%quiz;

__DATA__
1. What is my name?
A. Rooney *
B. Gerrard
C. Ronaldo
D. Ronaldinho
2. Who's your bet in the coming World Cup?
A. Brazil *
B. Germany
C. England
D. Cameroon
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You can then do things like: "What is the answer to question two?"

print $quiz{2}{$quiz{2}{answer}};
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or, "Display question 1:"

print '1. ',$quiz{1}{question},"\n";
for ( sort keys %{$quiz{1}} ){
    print "$_. ",$quiz{1}{$_},"\n" if $_ !~ /\p{Lower}/;
}
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or, "Display them all:"

for (sort keys %quiz) {
    my $number = $_;
    print "\n$number. $quiz{$number}{question}\n\n";
    for ( sort keys %{$quiz{$number}} ){
        next if /question|answer/;
        print "$_. $quiz{$number}{$_}\n";
    }
    print "\nAnswer: $quiz{$number}{answer}\n";
}
[download]

Update: or a little clearer:

for (sort keys %quiz) {
    my $current = $quiz{$_};
    print "\n$_. $current->{question}\n\n";
    for ( sort keys %{$current} ){
        next if /question|answer/;
        print "$_. $current->{$_}\n";
    }
    print "\nAnswer: $current->{answer}. $current->{$current->{answer}
+}\n";
}
[download]