Kitchens are dangerous places,
Particularly for a child who can't see over the bench tops, and there are many hazards to avoid. To make the kitchen a safe place to work, you must set out clear guidelines for your child to work with. Consider implementing rules for:
Children under the age of ten generally don't have the fine motor skills to safely use a sharp knife. If your child is under five, keep him away from knife duty completely, but if he's older and is keen to try using a knife, offer him a plastic knife or butter knife and something soft like a banana or bread, or he could try making his own sandwich with a knife.
Children must be closely watched at all time when using electrical appliances. They can too easily be tempted to put their fingers into fast moving beaters or blades.
Stove and oven
Generally, a good rule of thumb here is 'don't touch either ever'! When in use, stoves and ovens are obvious hazards in the kitchen, but very often they can stay hot to the touch for some time after you've switched them off. If you always keep your kids away from them - hot or cold - then they'll never risk burning themselves.
Again, this is an area where you should just have a blanket rule that your children are not allowed to deal with hot or boiling water. Carrying a pot of hot water to the sink can be a perilous business - there's the steam that can suddenly be in your face, the weight of the pot, along with the unexpected heat of the handle to watch out for. Most children aren't good at carrying heavy objects, even for a short distance, so don't let them do it at all.