The city is certainly not "kid-friendly" at all, but there's plenty for kids to enjoy.
Cirque du Soleil
The world's most famous Cirque du Soleil (www.cirquedusoleil.com, 3300 South Las Vegas Boulevard, +1 702-894-7722) - note that only humans perform here, no trained animals for kids.
Walking around the city
A sort of amusement park in Las Vegas is Fremont Street in Downtown. In the evening, it turns into a giant and totally free colorful show. It is arranged as a huge pedestrian area with a ceiling that is a digital screen.
Performances
The city regularly hosts dance shows, magicians, and concerts.
Few people seriously seek out entertainment for kids in Las Vegas, but if you happen to be in town with little ones, take them to the circus and pirate show at the Treasure Island Hotel (3300 South Las Vegas Boulevard). Check out the musical fountain show at the Bellagio Hotel (3600 South Las Vegas Boulevard) and the Volcano Eruption at the Mirage Hotel (3400 South Las Vegas Boulevard).