Two possibilities:
1) Shorted diode(s) in the alternator. The alternator will still charge the battery when the engine is running, but it will drain the battery when stopped.
2) One or two bad cells in the battery itself. A healthy lead-acid battery produces ~2.1 volts per cell, so the nominal battery voltage (measured at the battery with a good meter) after sitting overnight should be ~12.6 volts. If you measure ~10.5 volts at the battery after it has been sitting a while, this suggests that one cell in the battery has probably failed. Next, measure the voltage at the battery with some load (e.g. lights or ignition switch on); the voltage should drop slightly, but not a lot. Finally, measure voltage at the battery when cranking; it should drop no more than a volt or two. Any voltage measurement less than 12 volts that is an approximate multiple of 2.1 volts may indicate one or more failed (or failing) cell(s).
As
Ogre has stated, a bad battery or alternator will often cause the other to fail, too.
[This message has been edited by Marvin McInnis (edited 06-27-2008).]