AllSongsBy is a free service that lets you listen to music in streaming. The site is based on the catalogue of YouTube and you can listen to individual songs and entire albums of music. It's a search engine but on the main page but you can already find a list of the most listened artists or you can choose a genre. The site is simple and organized, you can also buy songs for iTunes or create a playlist on a web page using the embed code. Registration not required.