Foobar is mentioned everywhere. While it's not my player of choice, it has been considered one of the best, most lightweight and customizable players for a long time in pretty much any discussion about audio players for Windows.

Yeah I use it now, I just wish it was updated one more time to add some OS-level polish to it (like getting taskbar integration on Windows 7 an above without a plugin).

The actual look of the application doesn't bother me, since usually I'll be working on something else that needs the screen space.

There has been some interesting work on the Foobar 2000 "Mobile App", including a version of Foobar 2000 in the Windows 10 Store. It's interesting to see the work done on that version. Supposedly there was going to be a Patreon or Kickstarter to push that work even further but I don't recall what happened there or didn't follow it well enough.

Also, I think that effort was before the modern Windows desktop "bridge" and it would be interesting to see an attempt at a "best of all worlds" version for the Windows 10 Store that supported all of the Desktop features and all of the "Mobile" features (such as Windows 8+ background audio controls).

according to wikipedia there are a windows phone, ios and android versions out right now.

foobar2000 might be customisable, but it comes with terrible defaults in comparison to WinAmp UI-wise. I've tried foobar2000 a few times, but I never have the energy to make it work nicely.

foobar2000 replaced winamp for many of us.