How many ohms do you need before you need a resistor?
You said that in the first test, where the LEDs blew up, you used a 4.5 volt battery.  That would force MUCH more current through the LEDs than the 3 volts you used in your second test.

The 3 volt test would still be forcing much more current through the LEDs than their maximum rating, and may greatly shorten their life.

What you should do is:







simulate this circuit &ndash; Schematic created using CircuitLab

Since LEDs are not guaranteed to have identical forward voltages, if you connect two LEDs in parallel, with a common series resistor, one LED will draw more current that the other, so will get a little warmer, so its forward voltage will drop slightly, making it draw still more current....  which may cause one LED to be destroyed (not too likely) or one LED to be significantly brighter than the other.