My skype password was recently changed. I've changed it back and found it in the internet on hacker's site. My password is pc-generated, like as2fZ12v. How did they manage to hack it, if I've never written it anywhere?
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Although Skype uses robust mechanism and cryptography to authenticate a user, a password can be compromised in many ways from many different points. For example:
In fact, there are so many different ways to compromise your password that one can not answer your question precisely.
Most of the time, attackers are able to obtain credentials on robust applications that they cannot compromise directly (e.g. Skype, Facebook, Google) thanks to password being reused on different applications and systems with weaker security settings.
For instance, when a big username & passwords list is leaked on internet, hackers immediately check for those credentials on other applications.
You can also check online tools that verify if your username / email has been compromised somewhere, for example: Have I been pwned