It's a very valid question, as it's a way for people to decide if they want to listen to what you do, but it's excruciating for this songwriter, at least. I listen to an incredibly wide variety of music, always have, and I think all of it has had a big influence on me even if you can't directly hear all of it in my stuff. On top of that, much of my inspiration is music that people think of differently than I do.
For example, the Grateful Dead have certainly had a large effect but they are mostly known for their long drawn-out jams, especially to those who have only heard a little bit of them or gone to a show or two. The thing is, what I love best about them is their own diverse influences and how well-written their songs are. They have a much stricter structure than most people realize and the jams, while free-flowing, were always within the context of that structure much like great jazz. Many current jam bands just jam, the songs are more like vehicles for jams than examples of great songwriting, and it's quite a different way to play, one that I don't personally enjoy.
Huge influence? Yes. Do I play music like theirs? Not really. If you like the Dead will you like my music? Maybe.
From folk to jazz to classical to show tunes to good ol' rock and roll from the 50s to today with lots of stops at music from across the globe, every piece of music I've ever heard has informed my style, even the music I don't particularly enjoy has had an effect by teaching what not to do. I've sung in church and secular choirs, performed in many musicals, trained in African percussion, and played with very different bands in my past. What I do now comes from all of it and separating out specific examples just doesn't make any sense.
Honestly, I think if an artist can pinpoint precise influences their music isn't very interesting. It's even worse if the audience can tell exactly where you are coming from. Music is a living beast that evolves just as we have evolved from single-cell critters to the complex species we are today.
If you tend to listen to just one genre, please go get something else and expand your mind, whether you play or write or just enjoy listening.