So, here is what I've done with my toddler. Ideas are below the ages.
15 MONTHSPudding painting. It was messy. It was chocolate. It was awesome. His favorite part (since he's not a fan of art yet) was the bath.
Cooking with beans, rice, or pasta is always one of Hayden's favorite activities. He gets spoons, pots, measuring cups, and bowls. We also get creative and put the pasta/beans/rice in his Legos, Play-Doh, and anything else we can come up with. No joke, this keeps him entertained for 30-40 minutes at a time. Supervision is required. So long as there's a binky in his mouth, he's not likely to "taste" what we give him, but I've had to make that grab a couple of times when he's been tempted. Bonus: giving him the broom to "sweep" his mess. It usually makes things worse, but it's another five minutes of entertainment. Also, I realize this is messy, so we keep it on the hard floors as much as possible. Even when it carries over, there are far worse things in our carpet than beans or rice. (Have you SEEN a close-up of a dust mite?!?)
Contact paper taped to a window or wall with little shreds of tissue paper and/or crepe paper. Hayden had fun shredding the paper and sticking it to the contact paper. This kept him entertained for about 40 minutes, if you include clean-up time. He loves throwing things away in the trash.