I often listen to my own music for a number of reasons.
1) Tracing progress and remembrance
For me, listening to music that I've composed long ago is like visiting an old friend. Almost every piece that I write has some emotional relevance, and I associate different pieces with what I was experiencing in life during the time of composition. Listening to those pieces is akin to reading a diary. It offers me a glimpse into who I was back then emotionally, musically, and otherwise. It also allows me to see how far I've progressed in skill.
2) Finding new inspiration
My oldest pieces were written before I had any significant concept of music theory and form. When I'm stuck in a rut, I can listen to those pieces and hear things that I wouldn't likely do anymore, and those ideas are often refreshing. They came from a time guided by pure intuition. I'm not meaning to knock music theory- I love it and it has helped me tremendously. Listening to old pieces though can reveal chord progressions that I've long forgotten about. It can bring renewed creativity.
3) Completing old works
Often times, I'll work on a project and feel like it's gold. Then I'll get so stuck that I'll move onto something else. Years later, I'll hear the old WIP and think, "Man, that has some potential." With increased skill that has been developed over time, as well as being away from that old project for a long time, I'll be able to complete it and make something refreshing. This is especially handy when I have no ideas for new songs. I can go back and rework old ones.
In addition to all that, I simply like some of my old work. Sure, it's unrefined, unpolished, and I didn't know diddly about mixing (still don't know much...), but there are a number of good, raw ideas. And I write music that I like in a style I like. I can't quite find that anywhere else.
To clarify though, the bulk of music that I listen to is not mine. Every few months though, I'll go on a sudden binge listening to hours of old works.