MIDI Software
MIDIs aren't as popular now as they were 30 years ago (I can't believe I just typed that!) and unfortunately, there isn't a lot of modern software around that can play these files. Here's what I could find after searching around for a bit:
Winamp
My go-to MIDI player has always been Winamp 2.x with the MIDI plugin installed! It still works on Windows 10 (not sure if it does on Windows 11) and it has lots of features and skins.
Winamp v2.95
MIDI Plugin - Place this .dll file in Winamp's Plugins folder!
Cynthia
I haven't tried this player out personally, but it looks nice and it's free! Download it here!
Soundfonts
Playing these files normally will use the default instrument synthesis on your computer's sound card, and most of the time they won't sound very good. Many of these MIDI files were sequenced with specific sound cards or external audio hardware in mind, like the Sound Blaster 16 or Yamaha XG. You can use soundfonts to make your MIDI files sound better!
CoolSoft Virtual MIDI Synth
This program allows you to load soundfont files for different sound cards or audio hardware. Once loaded, you can play MIDI files with any player and they will sound like they're playing on a specific sound card! You can also convert your MIDI files to .wav format using whatever soundfont you choose, and convert the resulting file to .mp3!
CoolSoft Virtual MIDI Synth v2.10.1
Sound Blaster 16 Soundfont - Part 1|Part 2|Part 3|Part 4
Roland MT-32 Soundfont - Part 1| Part 2| Part 3| Part 4| Part 5| Part 6| Part 7| Part 8| Part 9| Part 10| Part 11| Part 12| Part 13