Do you have to have music to practice or receive Reiki healing? No! BUT - if you're going to have music, make sure it's going to complement your healing - no Death Metal or Punk Rock! :)
Surprisingly, classical music isn't ideal either - it's usually too emotional or too dynamic. For Reiki healing, you want music that was composed for massage, healing, meditation, that sort of thing.
Putting on your favourite music gives your wellbeing a boost - especially if it reminds you of your last Reiki healing session!
Here's some of my favourite music to work with: