You haven't told the browser that there is an image coming. The only MIME type that you have given is "text/html", you need to drop all of the html and tell the browser to expect "image/gif". Take a look at the Downloading a file discussion, where there is discussion of headers similar to what you need to set.
Hint: You should take a look at the headers that you get back when you download the image from www.nhc.noaa.gov, and probably hand them back, or directly link to the noaa image from your existing html, like this: 
print STDOUT "<html>\n<head>\n";
print STDOUT "<title></title>\n";
print STDOUT "</head>\n";
print STDOUT "<body>\n";
print STDOUT "<img src=\"http://www.nhc.noaa.gov/storm_graphics/AT06/r
+efresh/AL0606W5+gif/144631W_sm.gif\"></img>\n";
print STDOUT "</body>\n";
print STDOUT "</html>\n";

[download]
Update: see the responses, above, from Joost and Melly.

In reply to Re^5: showing an image downloaded with LWP::Simple by RobPayne
in thread showing an image downloaded with LWP::Simple by Anonymous Monk

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