Need urgent help

Um, to put it simply, my laptop gets a problem where it suddenly shuts down itself without any notice.

Not system shutting down, but it just suddenly turned off, and I can hear some kind of clacking voice each time it shuts down.

Can someone please tell me what's wrong with it?

You must get a new battery. Battery's die out over time.

I don't think so, because I usually plug in my laptop and remove the battery, so it cannot be battery ptoblem.

I have to agree. Either your batterys out of power or rubbish or your laptops overheating so it has to shut down to cool off.

Overheating is indeed the most likely problem here.

It used to happen to me a while back, when the proc temp went to ~110°C.

I just cleaned it back then (with a vacuum cleaner, which may not have been the best idea, but it's still working perfectly fine).

Definitely not the best idea in cleaning a laptop. Because of that you actually create static in the circuit board which will damage your laptop.
Next time if you're going to clean up your laptop, go buy a can of compressed air at a computer shop. They work a lot better than a vacuum cleaner

Seconded. A can of compressed air is the safest and easiest way to clean out dust and cobwebs (yes, I have seen cobwebs in desktop computers) in computers. To use it on a laptop spray through the air intakes that are usually along the edge of the computer's case.
Also, what is the computer sitting on when it overheats? If it is just sitting on a bed it may help to get a cooling pad, or even just something to sit it on.

I always put my laptop in a cooling pad, and no, I think overheating is not the problem as well.

It turned off suddenly just a few moments after I push the power button, so there's no way it was caused by overheating, right?

Tell us what make/model laptop you have. I have had a similar issue with an HP dv9000. It turned out the motherboard was bad. Also try the forums on the manufacturers website, odds are someone else has had the same problem and has asked about it there. If it is overheating the only fix is to take it apart and clean the thermal grease off of the processor and reapply with new grease. When something is overheating, how long it takes to overheat tells you where to look. If it takes 30 seconds for the computer to shut off to save itself than it has something to do with the cpu/heatsink mating surface. If it takes 30 minutes to overheat it has something to do with the fans or the air passageways on the computer, usually being clogged with lint.

Fixed already. It turned out to be a problem in the power output or something, so when the power button is pushed, it get shut down forcefully right away. Defective product, so I get my full warranty.