They spontaneously do things that I never could have foreseen, that I never could have expected. Just last week, my nearly-4-year-old, T., was eating a bowl of cereal with milk at the table and while I was doing something else in the kitchen, she spontaneously decided that it would be a good idea to put her bowl of cereal, milk and all, in her toy shopping cart and push it into the living room, because she'd rather eat there. When I discovered the mess, I was laughing way too hard to be even remotely upset, because that is something only a little kid would do. I cleaned up the mess and explained gently why that isn't the best idea, and asked her not to do it again.
The other evening while I was in the shower, with the door locked to the master bedroom, so no one would come in and tear apart the bedroom or pound on the door while I showered, my husband watched the kids. My 20-month-old, M., pooped and decided to solve this problem herself by stripping naked, sprinkling poop all down the hallway. My husband is very poop-averse, and I had locked him out of all the diapers in the house, by locking the master bedroom, so he had to deal with this spontaneous poop-mess and figure out what to do about diapering M. until I got out of the shower.
Then this morning, before a playdate, I gave the kids a bowl of Cheerios (no milk this time) to munch on while they sat on the couch watching TV. They ended up on the floor, naturally, and T. began stomping on them, yelling "Mommy! I'll save you from the evil Cheerios!" M. then wholeheartedly joined her in stomping Cheerios. Once again, it was entirely too funny to even get mad, so I got out the Swiffer Sweeper, vacuumed up the Cheerio-dust and asked them to please not do that again.
As you can see from these examples, there's tons of spontaneity after having kids! It's just driven by them, instead of by you. Thankfully it's not all messy or smelly... they give lots of spontaneous hugs and kisses, too, and those are the best.