Today I let my car battery charger charge a car battery over about 8 hours and probed the voltage to be about 15V with still 2 amps being pumped through by the charger (though the current was slowly falling over time) Is the battery damaged? The charger is a standard one designated for car batteries not an improvised one.
I take it that the "car battery charger" you mention in your post is an old-school type, which does not have any built-in charge regulation?
If it's taken your battery up to 15 volts, and it's a modern, regulated charger, it appears to me to be faulty. After 8 hours, no self-respecting modern charger should still be charging at 15 volts. If it's old school, this is pretty normal, and it's time to stop charging.
So, to answer your question, Yes, 15 volts is too high. Most car alternators, that normally recharge your battery after every start, and provide power while the engine is running, are normally voltage regulated to about 13.8 to 14.0 volts. Up to this voltage and at normal temperatures, the battery will only gas very slightly. Above this, and it will gas increasingly with increasing voltage. This will damage your plates by causing flaking of plate material and shortening your battery's life. Gassing is undesirable.
Note, by gassing, I don't mean boiling. Gassing is the breakdown (electrolysis) of water (H2O) in the electrolyte into H2 gas and O2 gas. This happens when the plates cannot accept any more charge (I.e. there is no PbSO4 left to be converted, meaning the plates are fully charged) if the voltage goes too high. A regulated charger will hold the voltage to 13.5 to 13.8 volts once the voltage has peaked, to prevent gassing and overcharging, and the current will drop to almost zero in a healthy battery. Gassing due to overcharging also "uses up" the water in your electrolyte, and in sealed batteries will fairly soon ruin the battery. You may have also noticed that the battery started to get warm/hot. This is another sign of overcharging, and is also damaging to the battery due to expansion and warping of the plates.
CAUTION: This gas is a highly explosive mixture, so be very careful not to create any sparks near the battery while gassing continues, or for a while afterwards. Battery explosions are very nasty and dangerous. You'll get debris and acid flying in all directions.
I can't answer as to whether the battery will have been damaged. If it got hot, it may have been. If the electrolyte level has gone down, it will need to be topped up with distilled water. About 10-12mm (1/2 inch) above the top of the plates is about typical, but wait until gassing has stopped, then rock the battery back and forth a few times to release any gas bubbles from the plates first.
To find out about the state of your battery, either get it tested, or put it back in the car and see how it goes.
Hope this helps!
The 15V is not a real reading. It's an artifact of bubbles formed on the plates from overcharging, which have by themselves an anode and a cathode. This creates a false" voltage potential that really isn't there. (Well, technically it's there, but the bubbles are acting as tiny cells in series, but have no actual stored potential. A high impedance DVOM is not enough load to break down the bubbles, so you get an exaggerated reading of Open Circuit Voltage (OCV) that is not a good indication of true State of Charge (SOC).
A quick way to verify this is to load the battery to some extent, breifly, which causes the bubbles to burst or release from the plates. I use an automotive headlight bulb in a socket for a minute or two. Check again with a DVOM, and you will find your 15 volts is now 13.2 or something - much more accurate and indicating the battery is fully charged -- not damaged.
Only extended over-charging that boils away the electrolyte has the potential to damage the battery. Your best solution is to buy an intelligent charger that watches various parameters and ramps down the charging toward the end.
15vdc is borderline too high. First of all, unplug the charger if you haven't done so already. Next, check to see if there are any visible signs of a boil over. Be careful if there is, because this is acid which can burn you. Next, probe the battery at the terminals with your multimeter to see what the voltage is reading. If it reads somewhere in the mid 13vdc without the charger on it, you're probably in okay shape. Really, I doubt you've done too much damage to your battery, but it's definitely not good. Remember, though, the charger will be above 12vdc in order to charge the battery, so this is the reason it was looking so high I'm sure.