I used to run with a Sansa Clip. It was perfect for that use case. Tiny, practically weightless, and could store many hours of music. My computer treated it like any USB drive, so it was easy to update. One of mine (I think I burned through 3 of them over the years even had an FM radio.

Today, when I run, I just carry my phone. It ends up doing everything the old clip did but in a much larger and more cumbersome package.

I'd probably carry my phone anyway these days after having a run, years ago, where my IT band told me I was done NOW but I was 8 miles from home. It was early Sunday morning and I ended up walking 2 miles on country roads and then through an empty office park before I found some place with a phone to call for a ride. That sucked.