Why my LED dies when connected directly to a 9v battery?

alnath:
I think that a datasheet like this one datasheet (there are plenty of them) gives you all the answers you need. You might want to have a close look at the curves, especially the "Fwd Current vs Fwd Voltage" one .

That's indeed what i'd expect reading that diagram the ideal voltage is 3.5 V, but starting at 2.7V the led starts giving a current, and emitting light. So If you put 2 of these in series, and apply 6V to it, they'll both light up, but the current will be about 4mA, and so they will be pretty dim, and each will have a voltage drop (and at that moment forward voltage) of about 3V (small differences between the leds are of course possible). Even though their ideal forward voltage to reach their 20mA is 3.5V.
I think i'm understanding it very well?