In the first movie when Jim wonders why Herbie chose him:
Jim: What I don't understand is, out of the millions of people in the world, why it picked a dogeared second-rater like me.
Carol: You stood up for it once. I guess it thought you were...worth belonging to. I understand that.
(Note: They get married at the end, Herbie is The Love Bug after all!)
In Herbie Goes To Monte Carlo Herbie is trying to impress Giselle, but he's dirty and acting like such a lovesick goofball that she'll have nothing to do with him. Only when he cleans up, gets some flowers, and tries a more subtle approach does he succeed.
Herbie falling in love in Herbie Goes to Monte Carlo, especially near the end of the big Trans France Race where the plucky Bug rescues Giselle from being wrecked in a river. They then spend the night after the race watching the fireworks over Monte Carlo.
In the 1997 remake, after Herbie is rebuilt everyone is so worried that Herbie won't "wake up" when Jim starts the ignition that they take a moment of silence. Then the car starts and Jim asks if Herbie is there. Herbie honks in joy and everybody is so relieved!