WALL-E doesn't smoke, but he collects lighters. They're one of the many objects he hoards, and he shows EVE his lighter collection when he brings her into his little home. She ignites the flame as a love song plays, singing "That is all that love's about." Even robots can see how the flame of the lighter represents the flame of love kindling between them.
When EVE is out of commission WALL-E lights the lighter to try and revive her, but the wind blows it out. With EVE powered down, their relationship isn't going anywhere.
We see the lighter in the movie one more time, in the dump aboard the Axiom. It reminds EVE that WALL-E's parts are on Earth, and if she returns there, she can repair him. And the final time we see the lighter is in the credits. A flick of the lighter and, boom, let there be light illuminating the credits. EVE may be able to turn on light bulbs like Uncle Fester, but there's something charming and rustic—like humans ditching technology and returning to farm on Earth—in the bright flame of a lighter.