I am reading Paradise Lost again at the moment, and I find it intensely enjoyable. I would recommend it because the imagery and description is awesome and strange. On the debit side, it's all about theology and the theology is crazy. But you can read it as bizarre science fiction. It's very stirring.
A more accessible verse novel is The Ring and the Book by Robert Browning. That is the story of a 17th century Italian murder, told like Rashomon by several different unreliable narrators. It's a good story, and Browning compared to Milton is sane and liberal and tolerant.
And another Victorian novel is Aurora Leigh by Elizabeth Barrett Browning. I think it was possible for a woman to get away with a slightly more racy premise in verse than in an ordinary prose novel. Aurora Leigh is a woman who makes a living as a writer, and sets up home in Paris with another woman who has escaped from prostitution. It's not massively unlike Jane Eyre.
And a recent verse novel I have read is The Broken Word by Adam Foulds, which is an account of the Mau Mau rebellion in Kenya, and the atrocities committed in reprisal. Here is a very short extract in the Guardian.
A shorter verse story, perhaps a verse novella, is The Rime of the Ancient Mariner. I think it was influential on Poe and hence Lovecraft, and ultimately all the Antarctic-set stories such as The Thing. I enjoyed reading this as a child, so I think it is the most accessible story in verse. I also loved the verse-novel Hiawatha as a child, but am not sure if I would still like it, it's been years and it might come over now as more than a bit patronising to Native Americans.
I only post these recs because I was strongly disinclined to read any of them, but then I liked them all, and I was glad I had read them. (ETA - has anyone any other recommendations?)