[tomkarho]

Being a faithful user of keepass and it's variants, I see no problem with offline managers like that and I would always recommend those over any other manager. That being said, if password managers are not your thing, you really have only one option.

Your own memory.

More precisely, create pass phrases (emphasis on phrase meaning: multiple words) based on certain characteristics only known to you that are relatively easy to remember by you and you alone. One trick is to use a common base phrase and then based on the service/app etc. you pick some characteristics of it to enhance the base so your full password would be [base-phrase]+[your-service-specific-parts]. Kind of like semi-analog version of a password and a password salt. Of course, if someone cracks your base phrase you are SOL so even that is not foolproof.

Either that or invest in memory palace techniques to make yourself supermemory so you remember every random password like yesterday.

Or third: get whacked in the head real hard so your brain rewires itself and you develop photographic memory and never forget a thing (yes, this one is a joke).