perl -ni.bak -e 'print if /\S/' file1 file2 ...

Update:To the benefit of speed too:

#!/usr/bin/perl -w

use strict;
use Benchmark qw(timethese);

my @data = ("sponge\n","\n",
   "wibble\n","boing\n",
   "spam\n","\n"," spud\n"); 

my $nsre = qr/\S/;
my $isre = qr/^\s+$/;

timethese(1E6, {
   'nospace' => sub { grep {/$nsre/} @data; },
   'isspace' => sub { grep {!/$isre/} @data; }})
[download]

Resulting in:

Benchmark: timing 1000000 iterations of isspace, nospace...
   isspace: 67 wallclock secs (56.34 usr +  0.15 sys = 56.49 CPU) @ 17
+702.25/s (n=1000000)
   nospace: 63 wallclock secs (49.19 usr +  0.26 sys = 49.45 CPU) @ 20
+222.45/s (n=1000000)
[download]

Unless my dataset is unfair.

--
¤ Steve Marvell

If you're talking about quarter mile times (i.e. Perl Drag Racing), then the only way to fly is:

perl -ni -e 'print if length > 1' file1 file2 ...

Of course, this '1' might be '2' if your platform uses CRLF instead of LF or CR alone. You people know who you are.