Minecraft 1.6.4 and older
Minecraft versions using the legacy asset system (1.6.4 and earlier) no longer play any sounds.
This is a launcher issue and not a game issue because in my modded setup of 1.6.4, any sound assets from mods still play but any vanilla sounds do not. I have tried on vanilla as well (versions tried and affected: 1.6.4, 1.5.2, 1.4.7).
From the log, it looks like Minecraft is actually loading the files correctly, however there is no sound being played. Here is a snippet of the logs since JIRA is preventing me from actually attaching any files:
18:20:48 launcher Local file C:/Users\<username>\AppData\Roaming\.minecraft\assets\objects\af/afb01196e2179e3b15b48f3373cea4c155d56b84 has filesize of 8985 bytes
18:20:48 launcher Preparing wood2.ogg
18:20:48 launcher Preparing wood3.ogg
18:20:48 launcher Got local file for wood2.ogg
18:20:48 launcher Got local file for wood3.ogg
18:20:48 launcher Local file C:/Users\<username>\AppData\Roaming\.minecraft\assets\objects\1e/1e82a43c30cf8fcbe05d0bc2760ecba5d2320314 has filesize of 9150 bytes
18:20:48 launcher Local file C:/Users\<username>\AppData\Roaming\.minecraft\assets\objects\27/27722125968ac60c0f191a961b17e406f1351c6e has filesize of 9368 bytes
18:20:48 launcher Preparing wood4.ogg
18:20:48 launcher Preparing wood5.ogg
18:20:48 launcher Got local file for wood4.ogg
18:20:48 launcher Got local file for wood5.ogg