The single reason to shred documents is to destroy the information that the paper contains. There are a myriad of reasons to keep thing private but in the end the shredding process is the same. If it was not important it could just be set out to be recycled and the shredding step could be skipped.
The first question for any shredder is how secure is the process. If the information can still be recovered it doesn’t meet the primary function. Some people have gone back and forth on the difficulty in re-assembling shredded paper.
Some shredded pages are easier to put together than others. Strip shredding comes to mind. The famous example of this is the Iranians using tape to put CIA documents back together in embassy after the revolution. But it has also been used by thieves here in the states.
Cross-cut shredders are more difficult but not impossible. It is beyond most people with some tape but that is where computers come in. DARPA had a challenge to see how hard it was for a computer to do the re-assembly. A team was able to take pictures of shredded paper and solve clues that were posted. It is easy to imagine that this is being improved to be more robust.
While it is unlikely that you need to worry about the government using high powered computers to target your information that doesn’t mean that you shouldn’t take some simple steps to keep your information as secure as reasonably possible.
The first is to cut the paper into more pieces. Never use a strip cut shredder as it provides limited security. The more pieces you have the more difficult the project. So to have more pieces then do more shredding at the same time so it is all mixed up before it is put out in the recycle bin.
Even better than a shredder that cuts is a shredder that tears. This completely destroys the information on the edges rather than making a clean cut. This can be done with a hammer-mill, grinder, or a pierce and tear type shredder. The good news is that these technologies also scale very well.