The refrigerants used in refrigerators are gasses which can damage the ozone layer, poison the environment, or cause cancer. If the fridge is punctured (by being squished into a landfill, for instance), these refrigerants will leak out. Many of the insulating foams used in older refrigerators are also poisonous, or may be expanded with gasses damaging to the ozone layer. In most places, landfilling a fridge without removing the refrigerant and insulators safely is illegal. Give your local council a call, and they should be able arrange for your refrigerator to be disposed of safely and responsibly, usually for free (or at most a nominal charge).
Leaving the fridge out to be collected opens up another can of worms: children love to go exploring, and it's quite possible that one could get stuck in your fridge. Fridge doors are heavy, and have an airtight magnetic seal, making it difficult to get out of, and easy to suffocate in. Leaving all the shelves in place makes it difficult for a child to fit in, and taking the door off completely renders the appliance harmless1. Most fridge doors can be removed by unscrewing the top bracket, and pulling the hinge pin out. This is usually easy to do, as most fridge doors are designed to be removed, and fitted the other way round.
Why bother? Under many legal systems, it is an offense to act irresponsibly, such that you might cause harm to your neighbour. While leaving a fridge on the pavement is less obviously irresponsible than leaving a manhole uncovered, it is likely that the family of the deceased would have a good enough claim to take you to court, and it would be up to you to prove that they were negligent in the supervision of their child (and therefore it was their fault, and not yours), or that it could not reasonably be forseen that this would happen (and thus you were not irresponsible). Far simpler to avoid this risk by making the fridge safe in the first place.
1 - In studenty areas of town, there is often a thriving 'second hand market' for appliances, whereby anything waiting for collection is fair game. If you're leaving your fridge for others to reuse, I'd suggest either securing the door so it can't be opened (with something child-proof like a cable-tie), or detaching in and leaving it nearby. If it is of high-quality and in good working order, it may be better to donate it to a charity shop specialising in white goods.