One of the reasons I choose to homeschool my children is to create a much closer relationship with them than I had with my older three. My kids are closer to each other and to me.
It's hard NOT to be close to the kids when I'm their mother, their teacher, their chauffeur.... Because I'm the one that's always there, I'm the one they turn to all the time.
I also make a point of being emotionally available. Well, as far as I can be (I tend to be rather distant). When the kids need my attention, I try to give them my full attention and take care of them. The result is a much closer relationship than many families have.
Of course, I'm always open for ideas to create even more closeness. I love my kiddos and I love teaching them. It brings me such joy!