We have babyproofed to some extent, but haven't removed everything. The rubbish bin is accessible and I had 2 weeks where everytime she touched it, I said 'No Katie, we don't touch the rubbish bin, it's dirty, let's play with the blocks / rings / books etc' and carry her away. We had a few tantrums, but she knows now that she can't touch it. Sometimes I catch her looking at it, but I just say 'Katie, we don't touch the rubbish bin do we?' and she moves onto something else. We do the same with Daddy's DVD's.

She understands lots of what we say so that probably helps, but just letting you know what worked for us.

However if there was something around that was particularly dangerous (eg television she could pull onto herself) I would be insisting on it to be moved / barricaded to some extent.