It is no longer possible to get 3D sound in Minecraft (at least with the Rapture3D OpenAL driver – other 3D OpenAL drivers, such as those found on Creative or ASUS high end sound cards, may also be affected).
Replacing OpenAL32.dll and OpenAL64.dll in bin/natives per Blue Ripple Sound's instructions no longer has an effect. Replacing them in the Minecraft version folder results in Minecraft overwriting them on startup with default Minecraft originals, or no sound at all.
Rapture3D has a dramatic effect on the Minecraft experience, as detailed in MC-1037 by Matthew Kerswill:
You may be wondering how I am able to perceive any difference between a sound that is coming from above me and a sound that is coming from below me in Minecraft. The answer is that I'm using a drop-in replacement OpenAL device called Rapture3D, which can render a stereo feed for headphones that implements psychoacoustic cues based on HRFT data to make sounds "feel" like they are coming from exactly where they really are.
In case you're interested, Rapture3D is an OpenAL device made by Blue Ripple Sound. Codemasters distributes the "Game" version of Rapture3D with their racing games like the DiRT series (from DiRT 2 onwards) and the F1 series (from F1 2010 onwards). To use Rapture3D in Minecraft, you need to purchase either the "User" or the "Advanced" version of Rapture3D from Blue Ripple Sounds's website.
Here are instructions for getting Rapture3D working in Minecraft (as quoted from the Blue Ripple Sound website):
In "%APPDATA%\.minecraft\bin\natives", back up OpenAL32.dll and replace it with the rapture3d_oal.dll from your Windows system32 or sysWOW64 directory. The file will need to be renamed.
Version 12.5 and later of Rapture3D also include a 64bit version, which can be used with the 64bit version of Minecraft. Instructions are much as above, except you need to replace OpenAL64.dll with rapture3d64_oal.dll from your Windows system32 directory.
If you're not 100% sure if you're using the 64bit version of Minecraft (which depends on which operating system and Java Runtime you're using), you might want to replace both DLLs.