toolic hit the nail on the head, but you might choose a different delimiter so that it wouldn't be necessary to escape the forward slash, like this:

my $thing = 'foo/bar/goo';
( my $stuff ) = ( $thing =~ 
    m{                # Quote-like characters are now {}.
        ^             # Match at the start of the string.
        ( [^/]+ )     # Capture everything in the set of all
                      # characters that are not '/'
    }x                # Close the regexp. x modifier allows
                      # freeform (as in non-significant
                      # whitespace).
);
print "$stuff\n";
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The m{} brackets avoid the leaning toothpick syndrome in the original regexp. Of course if you were matching against a curly bracket the curly brackets wouldn't be all that wonderful as quote delimiters, but for this regexp they work out well. /x modifier added to allow comments and insignificant whitespace (it makes everything prettier).