haukex and choroba are both wise and right about possibly dangerous uses of eval but since you are asking the user to enter a regex you must be sure that is a valid one; infact your code allows to pass a wrong regex:

Gimme a string: a
Gimme a RegEx: a(
Unmatched ( in regex; marked by <-- HERE in m/a( <-- HERE / at .. line
+ .. <STDIN> line 2.
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So sometimes eval is useful and imho one these cases is compiling a regex (see qr// in perl documentation):

use strict;
use warnings;

print "Gimme a string: ";
my $str = <STDIN>;
chomp $str;
print "Gimme a RegEx: ";
my $pattern = <STDIN>;
chomp $pattern;

my $rex;
{ # a block to localize $@
 local $@;
 # eval the regex 
 eval{ $rex = qr/$pattern/ };
 # die if errors
 die "error compiling regex!" if $@;

} # end of the localizing block


print $str =~ /$rex/ ? "Yes!" : "No.";
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So do not avoid eval because it can be dangerous: know it and profit it! Obviously you do not use a bazooka to kill a mosquito.. do you?

PS about arbitrary code execution I was tempted to add also regex can lead to code execution but perl is wise in this: not arbitrary code:

perl -E "say 'match' if 'ec' =~ /$ARGV[0]/" "ec(?{print 'EVAL!';})"

Eval-group not allowed at runtime, use re 'eval' in regex m/ec(?{print
+ 'EVAL!';})/ at -e line 1.
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