I have been using Foobar2000 to play music on my computers for a long time now. It is fast, minimal and functional, but I sometimes find its UI to be sterile and not fun. Recently, I felt nostalgic for the fun times of WinAmp and started looking for modern clones of it. The best option I could find was WACUP (WinAmp Community Update Project). (Terrible name, and apparently it is pronounced wakeup.)
The software seems to be still in active development and only has preview releases for public use and beta releases for private testing. I went with the Preview v1.0.21.7236 - the download and installation were easy. I was able to invoke the player from the Start menu by typing either wacup or winamp.
Once properly customized, WACUP seems to feel just like the classic WinAmp, but updated for today. Though Preview, I have not seen any problems in using the player over the past month regularly.