Whenever I use a bow near a Creeper that is close to dying, the game hangs the moment I release the arrow. To close the game, I have to open task manager and try to end the Minecraft task. After a few seconds it returns as not responding. I can end it using the not responding window, but occasionally it returns a message saying Java has crashed and Windows is collecting info about the problem. When I restart Minecraft, I end up showing up where I was about 10 seconds before the bad arrow was fired. It's caused numerous deaths and holes in my world.
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Please see if there are any crash reports in /.minecraft/crash-reports/ and attach them here. If not please force a crash by pressing F3 + C for 10 seconds while ingame and attach the crash report here.
I didn't find any pre-existing crash reports from either Minecraft or Java/LWJGL, but I was able to generate one using the key combo you mentioned. However, my new PC currently isn't hooked to the internet so I'll have to wait until the wireless dongle for it arrives to upload it. Sorry.
This crash has also now affected my swords and axes. I cannot directly attack a Creeper now, I must either use lava, tag it and destroy it when it explodes, or skirt them altogether. I will try my hardest to get the crash report uploaded as soon as I can get an internet connection.

Maybe a sound file issue ?
Leave the game, delete the directory .minecraft/resources/ and restart, the sound files will be downloaded in the background (will take several minutes)
Edit: Just read your comment about internet issue.
Then rename the above directory to something else and re-test.
If the issue is gone, the you can delete .minecraft/resources/sound3/mob/creeper/ and .minecraft/resources/newsound/mob/creeper*
I don't have a speaker system set up yet (you can probably tell this set up was thrown together Christmas Day), but I doubt that would be the problem. I'll test the above fix now.
Here is the crash report I made a few days ago. Yesterday I did test deleting the sound files and the bug appears to be fixed now. I'll redownload the sound files and test again.