My kids used to ride with me. I used to take them on rides in the summer to the library, or to a place with big trees where we could climb up and I could read to them in the branches. What fun! The thing that killed it for us was when they got their driver's licenses!
My daughter is going away to college this year, and will be on a tight budget. She's talking about bicycling again! (And her boyfriend likes to cycle. Of course, she'll probably rather ride with him than me.
But he likes me and wants to ride with me, so maybe she'll come along!)