There is an alternative downloader for 64-bit editions of Windows here:
iTunes 12.1 for Windows (64-bit — for older video cards)
that seems to address the playback issues that some users have been reporting with the full 64-bit version (the alternative installer here is the same architecture as most previous "64-bit" versions of iTunes, i.e., a 32-bit application with a 64-bit installer). The "for older video cards" label appears to be something of a misnomer as some people have reported that this corrects problems found on current / high-spec systems.
Some users have reported that after installing this alternative version it is necessary to adjust the "Play audio using:" selection (normally to "Direct Sound" rather than "Windows Audio Session", though this may vary based on your audio hardware/drivers) in Edit > Preferences > Playback to restore glitch-free audio (one part of the reported symptoms is that the "Direct Sound" choice isn't available, usually in Windows 8).
Another possible remedy relates to a potential clash between the 64-bit version of iTunes 12 and Google Chrome; some users have reported that uninstalling Chrome (not just not having it running) resolves the iTunes playback issues without having to install the alternative version referred to above.
Finally, you may want to think about reverting to iTunes 12.0 - see Turingtest2's notes on Troubleshooting issues with iTunes for Windows updates for steps needed to completely remove all installed iTunes components, and for links to the 12.0 installers.
