One way to avoid long lines is go on rides that cater to larger capacities and can move people fast. This means you get to play faster. At Disneyland there are several rides where you won't be waiting more than 15 minutes. Including:
It's A Small World. This twenty minute boat ride around the world has lots and lots of boats on the canal. Your wait time will be short, no matter how long the line looks. Plus you can enjoy the sights and sounds outside the attraction with the kids as there is a show every 15 minutes.
Pirates of the Caribbean. The boats on this ride are six benches deep moving folks quite quickly. Add the fleet of boats that are continuously coming and your party will be seeing Captain Jack without much delay.
Disneyland Railroad. Many folks don't realize the railroad isn't jut transportation, it is also an attraction. Going all the way around the park gives you a glimpse behind the scenes as well as some great encounters with dinosaurs that the kids will love.
Jungle Cruise. Rarely a line at this attraction, but when there is it moves quickly. Loading up to 30 passengers a boat, most get the chance to see the back side of water within 15 minutes time of the joining the cruise.
Tarzan's Treehouse. The kids will love this unique look at the park and all the interactive features to touch and see. The only line you might encounter is the line looking at the instruments at the end, which won't be more than a minute or two otherwise walk right on!
Storybook Land Canal Boats. Loading lots of people on each boat to visit the enchanted stories, there is always folks lined up to take the ride. However the boats move swiftly and the lines keep moving so you see where Aladdin lives within minutes of the beginning journey.