Here is one way to do it by setting $/ = '' to read the lines in paragraph mode (see perlvar) and then substituting out the eol characters:

    #!/usr/bin/perl -w

    use strict;

    $/ = '';

    while (<DATA>) {

        next unless /\S/;

        chomp;

        s{\\\n}{}g;

        print "Line: ", $_,"\n";
    }

    __DATA__

    this is a good \
    nice day but not a good nice \
    night


    This is a test line

    This is a another test \
    Line




    This is \ a final test line
[download]

Which prints:

    Line: this is a good nice day but not a good nice night
    Line: This is a test line
    Line: This is a another test Line
    Line: This is \ a final test line
[download]

--
John.