Yes, use a password manager. Unless you're a password savant that can remember every character he's typed, you'll either be re-using passwords (a big no-no), or storing them somewhere. It's much more secure to remember one strong password and use randomly generated passwords everywhere.
I use Lastpass. They have synchronization across devices on their free tier, which is awesome. You can automatically import passwords from Chrome or Firefox. They even have a "security challenge" that will show you what repeated and weak passwords you're using. Lastpass also has some degree of automatic password reset on popular sites, which works pretty well.
