In Harper Lee's To Kill a Mockingbird, there are several clues that indicate that Boo is watching the children.
When the children are playing the "tire game" and Scout rolls into the Radley yard, she later admits that she heard laughing from inside. Of course, Boo leaves little gifts in the tree on his property for the children to find on their way home from school, until Mr. Radley cements the hole closed. At another point, the children see the blinds move in the house: had it been Mr. Radley, he would have come out to yell at the kids.
During the fire at Miss Maudie's, Scout ends up with a blanket around her shoulders, put there quietly by Boo to keep her warm. Jem's pants are repaired, sewn like a child might mend them, after Jem gets caught on the fence escaping from the Radley's yard.
Finally, it is only by keeping an eye on the children that Boo is able to save them from Bob Ewell when he attacks them at the end of the novel. Boo becomes an unlikely hero in this way.
The children exchainge gifts and presents with Boo using a knotholl in a tree. Eventually, this knothole is patched up by Boo's brother, Nathan Radley.
When the children are trespassing in the Radley's yard, Jem loses his overalls. They are returned mended and folded much to the surprise of the children.
During the fire of Mrs. Maudie's home, a blanket mysteriously appears over Scout's shoulders as she is watching the blaze. She never noticed that someone had placed the blanket there, but begin to think that it might be Boo Radley.
Finally at the end of the novel, the children are protected from the murderous attack by Bob Ewell after the Fall Festival as they are walking home from the school in the dark.
The children had never seen Boo Radley in person until the events of the attack on them in the school yard. After that the Finch children never saw him again.