As you get older, the awesomeness of Scooby Doo stays with you. It's funny to a 6 year old who likes seeing Shaggy and Scooby get scared and dress in funny costumes. It's funny to a 16 year old, who now gets why Scooby Snacks make everyone so hungry afterward. I'm significantly older than that now, but I still love Scooby Doo and here's why.
Velma. Velma is the ultimate Sceptic. No matter how scary the situation, no matter how much it seems like there really is a ghost haunting the abandoned Amusement Park, she keeps her cool and looks for evidence. Rather than accepting the supernatural explanation right away, she waits and looks for a natural explanation first. She applies her scientific skills and vast knowledge to seek the truth, and she always finds it.
It's not always easy for Velma to get to the truth. She has to deal with co-workers who immediately believe the irrational explanation and over-react, but she always handles them with diplomacy and kindness.
Velma is a great role model for kids, especially young girls who see a smart capable female character, who is rational and loves science. Velma actually wound up working at NASA which my young self thought was especially awesome (I really wanted to be an Astro- Physicist at one point).
If you want your kids to watch a cartoon that encourages critical thinking and looking for natural explanations before automatically accepting supernatural explanations, go for Scooby Doo. And sit down and watch it with them, it's pretty darn awesome.
I also liked Danger Mouse.