On the other end, they can contain important financial information or the like - which may benefit the heirs, or even other people.
When a brother (and associate) of my grandfather's suddenly died many years ago, among his legal and financial papers and records (including those about people he lent money to, or owed them), surfaced the letters he exchanged with his mistress. Of course my grandfather was uneasy, but it had a company to keep alive - and it's incredible how people you owed money immediately knock your heirs' door, while those who owe you stay well away (not everybody, sure, good people still exist). And you need the needed papers and record to settle things properly.
When you die suddenly, without time to prepare, it's a real mess. Heirs will need all the information to protect their rights. Unluckily, it also means some sides of your life you would have like to keep hidden may come to light. Just like life, even death is unfair, sometimes. Just, you'll never know.