My 7 year old daughter clings too much to me ...

my 7 year old daughter clings too much to me. after school/work, she hugs my legs and would not let go. she says that she glued herself to me. Almost every night, she grabs my arm or whatever part of me she can, and says "I need my mommy. i have to hold some part of you, I need my mommy".  i even gave her my old t-shirt to sleep with. I grew up with not much love, no support from my own mother (she said she'd send me away to play anywhere i want, because she wants to read a book). So I always imagined that I would be completely opposite. And I have been.  She has no prolem going to school/activities, but I wonder if this kind of attachment is normal? is it healthy?