KeePass stores all of your passwords in an encrypted file. The file can be shared with yourself across computers or with coworkers via Dropbox, OneDrive, or any other type of file share.
More importantly than keeping your passwords safe from other people, KeePass will keep them safe from you. You can automatically copy/paste username and passwords into prompts so you never even have to see your password. It also generates completely random passwords for you so you won’t even know the password in the first place.
All you have to remember is your master password.