I'll give you some by park:
Magic Kingdom - on your way to your afternoon break, stroll down Main Street, visit all the shops and make sure you buy some peanut brittle at the Confectionary. They make it fresh every day and it will run out! Disney wants to fill up all parts of the park, so there's a lot of entertainment there, too. Make sure you see the Dapper Dans and the marching band.
Watch the parades from Frontierland or grab a table at Sleepy Hollow and have funnel cakes while you're waiting. Pull up your stools right to the railing and you'll see the parade clearly and comfortably.
Epcot - go through Innoventions and do it all. There's a ton of fun stuff in there for kids, it's in the air-conditioning and makes it all fun!
Spend an evening in Future World. Everything is open until 9 except Innoventions and a couple of smaller things. It's one of the most beautiful parks at night, with the beautiful colors of Spaceship Earth all around. And usually much less crowded.
Watch the Jammitors. They're awesome!
DHS - on a non-Fantasmic night, make sure you go into the Animation Building by around 5:00. You'll see more characters in an hour than you would in a week. LOTS of different ones and Sorcerer Mickey too!
Take a drawing class in the Animation Building if your kids are old enough to sit still and try to follow directions. If not, save that for when they're older.
Animal Kingdom - do the Safari as early in the day as possible to catch the animals at their most active. Go through the "treks" in Africa (gorillas) and Asia (tigers) for close-up views of some awesome animals. Go slow, see everything.
Pizzafari almost always has seats available - there's a ton of rooms.
Don't forget to spend some time enjoying your resort. There's usually some sort of kids activities around the pool, some resorts have more than others. For us, the resort is as much a part of the vacation as the theme parks.
Get the photopass offer and get lots of photos your first trip of your whole family together. Wear 1st Visit buttons - the photographers will take more candid pics. We got lots more of waiting and interacting with characters, for instance, on our kids first trip. Some of those are the best ones.