We had many of the same issues that started at about the same age. I basically removed everything that I knew I didn't want DS getting into, locked a couple of cupboards, put the rubbish bin in the laundry sink, then decided to let him explore as he needed to. I found that mostly he got bored with things after a few weeks, and then it wasn't such a problem. I still said "no" to things, but by removing what was important/dangerous, it just meant that I wasn't saying "no" for the entire day.

I think it's not so much that they don't listen, it's just that as toddlers, they don't have impulse control like adults do, it takes around 3 years and loads of parental patience & consistency for this to develop (according to Pinky if I remember correctly).