While it seems unlikely this is the direction Amazon's show will go in, since they're already talking about a multi-season series, there's something particularly attractive about the prospect of an anthology series within Tolkien's world. There are a number of stories that could be told in a single season of TV, and it'd be a way of doing that and exploring different aspects of the mythology without bloating things over multiple years.
Peter Jackson's trilogy, an excellent (if not perfect) adaptation of the Lord of the Rings series, runs to around the same length as a 10-episode season of TV would, and there's something to be said for not going beyond that.
The Silmarillion, as an example, is full of great stories, but it'd take something truly special to pull it into a coherent long-running series. You could quite easily, however, adapt various stories within for individual seasons, and have some more overarching thematic links (or one or two recurring characters - both things Fargo has done brilliantly).
The story of Beren and Lúthien, The Children of Hurin, The Fall of Gondolin, The War of the Last Alliance, a season on Númenor and so on - there are numerous possibilities for a LOTR anthology that would deliver everything fans love about the series and be different enough from what's already been put on screen.
What do you want to see from a Lord of the Rings TV show? Share your thoughts down in the comments.