Valais is something of a dead end by nature: a fine expressway (A9) carries you in from Lac Léman, but to enter—or exit—from the east end, you must park your car on a train and ride through the Furka Pass tunnel to go north or under the Simplon Pass to go southeast. (The serpentine roads over these passes are open in summer; weather permitting, the Simplon road stays open all year.) You also may cut through from or to Kandersteg in the Berner Oberland by taking a car train to Goppenstein or Brig. A summer-only road twists over the Grimsel Pass as well, heading toward Meiringen and the Berner Oberland or, over the Brünig Pass, to Luzern.
To see the tiny back roads, you need a car. The A9 expressway from Lausanne turns into a well-maintained highway at Sierre, which continues on to Brig. Additional tunnels and expanded lanes are being carved out of existing highways. Distances in the north and south valleys can be deceptive: apparently short jogs are full of painfully slow switchbacks and distractingly beautiful views. Both Zermatt and Saas-Fee are car-free resorts, though you can drive all the way to a parking lot at the edge of Saas-Fee's main street. Zermatt must be approached by rail from Täsch, the end of the line for cars (there's a garage).