As side notes:

#!/usr/bin/perl -w
use strict;
[download]

Notice that nowadays (unless you have serious backward compatibility issues) it is recommended to

use warnings;
[download]

instead. Since when I made a similar remark somebody popped out asking why I thought the latter was a better alternative, I'll point out in advance that no, I'm not explaining it. perldoc warnings and perldoc perlrun give some clues about it.

my $jpg = shift or die "$!\n";

Huh?!? $! is meaningful only after a failure of a system call (well, "system library"). At this point it may be anything...

my $data = get_file($jpg);
my @res  = sizeJPG($data);
print "$jpg width $res[0] height $res[1]\n";
[download]

Please, do not misunderstand me: I know that this is a minimal example, but why do you put the return values of your sub into an array only to later use its entries separately? I.e., wouldn't have

my $data = get_file($jpg);
my ($h,$v)  = sizeJPG($data);
print "$jpg width $h height $v\n";
[download]

been clearer?

Also, in case the regex below is not matched, the return values will be undef, and this will issue a warning in the print statement above. And if you locally disable 'uninitialized' warnings, then you'll get an IMHO inconsistent output. You may want to treat this case in a different way...

sub sizeJPG {
    return unless $_[0];
    my ( $width, $height );
    ( $height, $width ) = 
   unpack( "nn", $1 ) if $_[0] =~ /\xFF\xC0...(....)/;
    return ( $width, $height );
}
[download]

I like to do

local $_=shift;
[download]

if possible, but that's just a personal preference.

As a general remark you can also use the return value of the match operator, but indeed in this case it can be slightly awkward:

my ($width,$height)=unpack "nn", (/\xFF\xC0...(....)/)[0];
[download]

and it will also issue a warning if the regex is not matched. So a possibly better solution may be:

my ($width,$height)=unpack "nn", /\xFF\xC0...(....)/ ? $1 : '';
# or "\0" x 4, maybe?
[download]

Let's go on...

sub get_file {
    open FILE, $_[0] or die $!;
    binmode FILE;
    local $/;
    my $data = <FILE>;
    close FILE;
    return $data;
}
[download]

Why not

sub get_file {
    local $/;
    open my $fh, '<:raw', shift or die $!;
    <$fh>;
}
[download]

instead?

(But then I'd probably use a do block. In the meantime we continue to wait for Perl6's .slurp!!)