"You need a new alternator" are words you don't really want to hear. If you take your Mercedes to a dealer then a new alternator, installed, is about $770.
But, mechanically, alternators seldom fail and many are still fine 30 years later. While it's possible the bearings may fail (and will squeel like a banshee) or the stator or rotor may fail it's not very common.
What is common is a failure of the voltage regulator and since the late seventies to the early eighties the regulator is a little doo-dad that bolts on the back of the alternator. They're about $18 new from mailorder/online places - probably more from the dealer. It's held in place by two 10mm nuts and can be removed and replaced very easily from underneath the car without jacking it up - at least on a W126.
Here's what the regulator looks like on the back of the alternator.
Now, if you don't want to run out and get a new regulator to fix your "broken alternator" you might well be able to repair the regulator itself. There's only two things that routinely fail on this thing - the brushes, which wear out as they're made of carbon (and are supposed to wear out) and the diodes. Frankly the diodes never seem to fail or at least I've never heard of or seen these parts fail on a Mercedes although I've seen plenty of Japanese ones fail. But the brushes are what usually go and they go rather slowly. At roughlt 200-300K miles the alternator light may start to flicker on and off as the brushes slowly make intermittent contact - that is they don't usually fail all at once leaving you with the draded red light on the dash on all the time signifying you no longer have an alternator.
Mercifully the carbon brushes are not that hard to replace. In a nutshell you have to first go get a set and any decent starter/alternator place will have them. They're the same for all BOSCH alternators so it's not possible to get the wrong ones.
You desolder the old ones, cut through the posts, install the new ones, solder them and you're done. That's it. Now just reinstall the regualator back on to the back of the alternator and you're done.
Here's some pictures from when I did this a couple of years ago.
Richard Sexton, August 2006