I've brought my 110 v stereo receiver from the US to Austria, and need
to buy a transformer. The receiver's manufacturer recommends a 1500
watt transformer. I've found one on eBay here, but I notice it doesn't
have a "3rd hole" for the ground pin of the receiver's plug. Can I
still use the transformer without sacrificing safety or sound quality?
The transformer itself is here:
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=5814230351&sspagename=ADME:L:RTQ:US:1

I would expect problems with "hum" from an ungrounded
power source.

I think sublime1 is right.

Check these articles on why you should pick a transformer not only
with a "3rd hole" but with a "3rd leg" too:

http://www.rane.com/note110.html

http://www.mhat.tv/documents/EngDox/HumBuzz.pdf

I Googled: three prong plug audio devices ground

Check other results there.

Yes you can use a transformer without a ground pin.  The ground pin of
your stereo receiver plug must be connected to "earth ground".  For
your personal safety, it is imperative that exposed metal -- the metal
chassis and enclosure of your stereo receiver; the metal enclosure of
a clothes washer, stove, etc -- be connected via a low-resistance path
to earth ground.

In the US, many older houses have 3-prong outlets but the ground pin
is not properly connected to earth ground.  Hence many people with
stereo receivers like yours, have (unknowingly) been operating these
receivers without a proper connection to earth ground.  Not
particularly safe, but very common, since over the years the
"old-fashioned" 2-prong outlets have been replaced with the "modern"
3-prong outlets (ungrounded).

To operate your stereo receiver with the transformer you describe,
simply obtain a commonly-available 3-prong to 2-prong plug adapter. 
The adapter has a small metal ring "tab", which should be connected to
the earth ground in your house's electrical system.  This earth ground
connection will also maintain all of the shielding in your stereo
receiver at earth potential, so hum will be minimized.