This gets my vote. I have a rule, "never use s/// when a tr/// (or y/// in this case) will do." I ran some benchmark tests a while ago on s vs tr and tr is much faster at deleting characters from a string. (This might be stating the obvious.)

I agree with kwaping, I would use tr/// for this solution.

#!/usr/bin/perl -w
use strict;

while (<DATA>) {
    chomp;
    tr/[]//d;
    $_ = join(" ",split " ", $_);
    print "$_\n";
}

__DATA__
[
 [ 0.039543323]
 [ 0.068993981]
 [ 0.086558227]
 [  0.12252527]
 [  0.14724698]
 [  0.16631099]
 [  0.18877556]
 [  0.20234162]
 [  0.18110326]
 [  0.13155017]
[  -4.0316574]
 [  -3.6178487]
 [  -3.1186917]
]
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s/[\[\]]//g;
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perl -lpi -e '...'
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ruby -ne 'puts$1if/(-?\d(?:\.\d+)?)/' < data > munged
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Update: To everyone griping and downvoting because it's not a perl solution, if you just change five characters (not counting s/ruby/perl/) it is valid perl. Have to leave something for the people asking extremely trivial questions yet providing no code of their own to figure out on their own . . .

(Hint: you need one more command line flag and change one keyword name)

Update 2: Awww, someone spoiled the exercise for the reader.

Translation to Perl:

perl -lne 'print$1if/(-?\d(?:\.\d+)?)/' < data > munged
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Update: I posted this before Fletch updated his node.

Sure you just need to use a regular expression. Open each file and loop over each line like this:

while( my $line = <IN> ) { 
    chomp($line); 
    $line =~ s/\[//g;   # Remove ['s  
    $line =~ s/\]//g;   # Remove ]'s 

    # Either print out to STDOUT here or 
    # write to another file 
}
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perl -lpi.bak -e 's/[\[\]\s]//g' files*
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As proof there is no such thing as a bad question, look at all the creative answers your "trivial question" sparked.

Now, there is such a thing as a badly-worded question, but yours wasn't one of those. :)