Okay, so you're creating a world. Does it need songs?
My answer would be yes, if you want to have a complete sense of world culture - but you shouldn't necessarily include them in your story. They should appear in the story only if they are doing something meaningful for the narrative.
Songs have an inherent difficulty to them - let's face it - because you can't really put the music into the book; only the words. But they can be very effective in creating atmosphere, and they can drive a story forward - or even do both.
Tolkien includes songs in his work. Along with the ruins and ancient places he puts in his stories, these suggest the deep history of Middle Earth. They also suggest the differing culture of the elves and the men. I think Tolkien's songs are great, but I love this kind of stuff anyway. Not everyone feels the way I do, and I know some people skip songs when they're added just for local color and world detail.
Anne McCaffrey uses songs as well, and I particularly liked the way she handled them in the Dragonsong/Dragonsinger/Dragon Drums series. Not only were they there to show culture on Pern, the songs were Menolly's central driving motivation, and there was an inherent conflict in the fact that the songs were used to teach lessons, but that Menolly's pursuit of music went against all the lessons she'd learned. That is a way to integrate songs thoroughly into a story! And come to think of it, that's the way I like to treat language in my own stories - on multiple levels.
Think about what songs - and the surrounding description of the music that you include with them - might do for the world you're creating. They can help to place the world chronologically, by invoking technology sets associated with the era in which those musical styles were typically heard. A story that includes lesson-songs has a very different feel from one that includes rock ballads, folk songs, etc. They can give emotional associations to a scene, or to the cultural group (elves, Harpers, etc.) with which they appear.
As with everything you choose to include in your story, I urge you to use songs with intent - not simply because it was fun to create them, but because they do something specific for the story as a whole. This function can be on the level of world alone, but you'll find the songs will be read by more readers, and enjoyed by more, if they can do more than this alone, but function on a plot and character level as well.
It's something to think about.