[Recently someone asked me which Borges stories they should read, and I thought my answer might be of more general interest.]
The following eight stories are the absolute core set of Borges's fictional works that you need to read. At least 95% of references to Borges will be to these pieces.
To these I would add the volumes:
Obviously, after these you can read the rest of the various collections. But the first eight stories are the creme de la creme.
As far as Borges's non-fiction, Seven Nights is possibly the most accessible. If you are a mystery fan, you might enjoy Six Problems for Don Isidro Parodi (co-authored with Adolfo Bioy-Casares) as well as the non-fiction piece "Chesterton and the Labyrinths of the Detective Story".
Copyright 2010 Evelyn C. Leeper.