This article is from the rec.audio.* FAQ, by with numerous contributions by Bob Neidorff others.
For tape decks and turntables, beware first of speed variations
(wow and flutter). A good check for this is Richard Strauss'
"Also Sprach Zarathustra" (aka: The Theme From 2001), which has
a long, low, sustained organ note that comes in well before the
main theme starts, and is held through the first movement.
Concentrate on that. Make sure it doesn't wobble or warble.
There's also a good bit at the beginning of Pink Floyd's
"The Wall", but it doesn't go on as long, so you've got less
time to think about it. Tape decks are prone to losing
high-frequency notes, so pick something you like which has lots
of treble, and make sure it is clear.
The sound of a turntable is largely bound up in the kind of
cartridge mounted on it. Make sure to listen to a table with
a cartridge similar to what you're buying, and not one in a
different price bracket. If possible, audition the turntable
with the same arm and cartridge, so that you will experience
potential cartridge/arm interactions, too. Most cartridges
work better with one arm than another. Treat the
tonearm/cartridge pair as a system, rather than independent
For CD players, try some piano music. See if the high notes
sound tinny. Also, try something which has some soft parts,
not the same as turning the volume down. Distortion for CD
players (as for other devices) is measured at a high output,
but in fact in CD players (unlike others) it's likely to be
worse in soft passages of music. Most classical recordings
contain a suitable soft passage. Most rock music won't.
Distortion in CD players, if you want to call it that, is
a function of the granulation noise, or time-delay pre-echo that
can come out of the filtering. To listen for this, use material
that is rich in high-order harmonics, such as brass music.
Unfortunately, you can't reliably predict how a CD player
will sound by looking at specifications, features, or the
technology it uses. If you want to know how a player will
sound, you MUST listen to it.