Jeannie Cox currently enjoys a flavor called Coffee & Cream when she vapes. She’s also fond of White Lotus, which tastes “kind of fruity.”

She buys those nicotine-containing liquids, along with her other e-cigarette supplies, at Mountain Oak Vapors in Chattanooga, Tenn., where she lives. A retired secretary in her 70s, she’s often the oldest customer in the shop.

Not that she cares. What matters is that after ignoring decades of doctors’ warnings and smoking two packs a day, she hasn’t lit up a conventional cigarette in four years and four months.

“Not one cigarette,” she said. “Vaping took its place.”

Like Ms. Cox, some smokers have been able to stop smoking by switching to e-cigarettes, and many are trying. A recent study by the Centers for Disease Control and Prevention found that more smokers now attempt to quit by using e-cigarettes as a partial or total substitute for cigarettes than by using nicotine gum or lozenges, prescription medications or several other more established methods.