Children usually get bored more quickly than adults, so if you're bored, there's a good chance the kids are, too. If they're having a blast and you're not, though, you may want to start hiking like a kid.
When children moan about how bored they are, engage in some group activities. Other entries on this blog provide a number of games and other activities that can be done with children on the trail.
If kids are older, allow them to bring a friend. It'll give you more time to spend with the younger children who may accompany you or at least give you more quiet moments to commune with nature.
Here's another clever solution, offered by Jim M., of Eureka, Calif., "Get them to talk about something they really like. This will require a little research on your part, so read up on their favorite video game, movie, rock band or television show, and ask some open-ended question about it. You're likely to get either a long monologue or if there are kids of similar age an impassioned debate about the matter at hand."
Read more about day hiking with children in the guidebook Hikes with Tykes.