PassGen is a completely free, no ads, app that allows you to generate complex random passwords using a customizable combination of alphabets, numbers and special characters.
Different combination ensures you get a completely random, complex string of characters for your password built on specified set of characters. It allows you to specify your own custom character set for password generation. Generated passwords can be copied to clipboard. Also if kept enabled, every generated password is kept in "History" tab for quick reference.
PassGen doesn't requests any additional permissions. Further, it doesn't have access to Internet and all your generated passwords are local to your phone and are as secure as your phone.