Sure they go bad.
But it might also just be the way that muffler was made.

Check for loose baffles by shaking it. Also look for rusty internals and holes in the baffles.

You could always buy a larger aftermarket muffler if you find a suitable one that fits.

Wise_Guy is really on the mark. Many Sears mower engines are ordered with the cheapest muffler available from the engine maker. If as he said about checking indicates the muffler is solid, replacing with an OEM quiet version will make the difference. Just make sure deck or external drive mechanisms allow for a larger muffler before buying a replacement.

Also check for a missing or damaged gasket between the muffler and the engine.

Thanks guys for the replies. I removed the muffler and shook it and didn't hear anything rattling around. It looked a bit rusty but nothing unusual. One thing I couldn't figure out was what is the purpose of the 3 small holes on the front face of the muffler, near the edges that are distinctly different in location from the grid of holes for the exhaust gases (see URL for pic). Great idea about the gasket. I didn't see one. But I don't see one on Sears exploded diagram of the engine either. I'll have to check that one out further. Thanks.

Here is a link that might be useful: picture of muffler

The Briggs engine on my departed mower had quite a loud exhaust, and replacing the original unit made no change in the noise level. Adding a much bigger muffler with a short threaded nipple took some of the bark from the exhaust.

Since it is a Briggs motor, go to a mower shop (not Sears) and ask them if one of the newer and much quieter Toro mufflers will fit.