Here are a couple of ways:

First, transliteration:

$string =~ tr{/}{\};
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Or with the substitution operator:

$string = s{/}{\}g;
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tr/// is going to be a little faster, but s/// would let you create more complex matching and replacing criteria.

For further reading, see perlop. There you'll find an explanation of the s/// and tr/// operators. Also see perlre for a more detailed discussion of what you can do with the s/// operator.

Update:Oops... yes, those pesky backslash characters need to be doubled up thanks to the gory details of quote parsing. tr{/}{\\}, for example. Sorry about that. ;)