indeed! even Tolkien was a huge fan of this! he has a very sizable body of work written in alliterative verse including re-tellings of the Völsungasaga and Atlakviða in modern english but retaining the same style as the original.
The alliteration ties back to the older forms of Germanic poetry, which had little to do with rhyming and a lot to do with alliteration and with clever ways of renaming things. Try googling "alliterative verse."