As cc260 mentioned, the alternators rarely are actually "bad". They might not be putting out the voltage, but often the only issue is that the brushes inside have worn down and are no longer making proper contact to conduct the electricity needed.
If there was no loud bearing squeal or audible grinding involved before the alternator stopped working, you might consider changing out the regulator brush assembly. It is about $30 and a 15 minute job with 2 small screws. it is worth a shot if the failure was just sudden and didnt included any drama like noises ot locking up and eatting the belt.
The part I am refering to is on the back side of the alternator and is usually a black metal round disk mounted on a white or grey palstic oblong plate with two screws, one on each end. Remove the two screws and rotate the assembly out of the alternator housing. The carbon brushes are inside and will be mounted on springs. You should be able to see the wear on them easily. Good luck.

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Christopher Henkel
1990 190E 2.6 - Arctic white SOLD
1986 190E-16v - Blauswartze
1993 300CE - SOLD
2003 W208 CLK 320 Cabriolet - Magma Red