Okay first off. I disagree with SCR who immediately suggests proffessional help for every problem here...
Before seeking professional help you should realize that this is absolutely normal behavior for a 4 year old. I've studied children's behavior for my thesis during the time I was studying to become a teacher of 2-4 year old children.
First of all children from the moment they learn to crawl, walk or any other means of moving themselves from one place to another without help have a whole new world opening up to them. All kinds of places and things to explore lay within reach now. So many doors to open with new mysterious things behind them. At your child's age everything is a mystery and he clearly loves to explore. Children between 2 and 5 years of age explore with every part of their body and every sense. They feel, listen, smell and taste everything and there is nothing wrong with that behavior.
I realize it can get dangerous when he climbs on things and opens every single jar. Here I have some solutions we applied to my very intelligent brother who was just like your son at that age opening everything even with child proof locks on them.
1. Because he is young he won't listen the first second or even 5th or 10th time. You'll need to keep telling him it's dangerous to climb. In some cases if he can't injure himself in falling, let him fall so he will realize the consequence of climbing is falling which leads to a painful behind or worse, but for now just knowing that climbing will lead to falling and pain when mommy isn't there to catch him is important. when he climbs on something low let him be and only catch him when he climbs too high and it gets dangerous.
2. The cupboards and closets are very interesting for a child and what's in it even more. What you want to do is keep all the dangerous things like cleaning detergents, scissors and the likes locked in one single closet that can be locked with a key. That way you won't have to worry about him eating or drinking something dangerous when he goes exploring.
3. What could help stop his closet raiding also is giving him 2 or 3 closets/drawers that contain his toys and belongings that you keep in the living room. That way you can tell him these are your cupboards and those are mommy's. Then by constantly reminding him that he can't open mommy's closets but allowing him to open the ones with his things in it, he'll slowly learn what he can and can not touch.
Over all it's a lot of repeating yourself. I've had parents say "I feel like a tape recorder. Over and over. don't touch this, don't do that, don't open that cupboard, don't eat that." so you're not the only one who's toddler doesn't pick up right away. The problem is often that parents think that their child should know better, but they forget that they are dealing with a 4 year old who doesn't see any danger and who doesn't pick things up right away. The key words in stopping this behavior are patience, persistence and repeating.
Have patience. If you feel you get angry put the child in his room and give yourself a time out. If he comes out put him back in. Be persistent in what you don't want him to do and putting him to his room if he does it after you said not to. Actions have consequences and your child is in this phase still learning the consequences of his actions. You are the parent so you need to be firm in what you say and do. If you say he'll get a time out if he doesn't listen give him that time out and put him back in his room if he comes out. Most important though and most tiresome for the parents is Repeating. He is only 4 years old and you will need to repeat perhaps thousands of times that he can't do something before he finally learns, but if you keep repeating it and show him the consequences of not listening and of his dangerous actions then in time when he gets older you'll see he'll learn. Don't expect his behavior to stop right away or for your son to listen right away when you say don't. After all when you were a child you were probably a hand full too and your mother and father had the same problems.
My advice. Lock all the dangerous things in 1 or 2 closets so your child can safely explore. Make sure he has no means to reach high places unless you're there to watch. Give him his own cupboard/closet/drawers to put his things in and take out when he wants. Above all Keep repeating the rules and when you say he'll get a time out give him a time out and make sure he stays. Make him understand with a lot of repeating that there are consequences to what he is doing. Letting him fall if it's from a safe distance where he won't severely hurt himself might help him understand this better. You'll probably feel tired and annoyed by having to repeat over and over but remind yourself that you're dealing with a child who doesn't understand yet that he's doing something bad or dangerous, to him it's just all about exploring and adventures in discovering his environment and it is at this age that you must repeat constantly the rules and show him what he can and can not do as many times as is needed until he gets it.