The big problem almost isn't your password itself but the quality of the security storing it. If a company stores all passwords in plain text in an easy to access database, your 20 random alphanumeric character password means squat now.
As for password themselves, either use a quality password manager or develop your own system for creating unique complex passwords for every important site.
For instance, start every password with a base of 8 characters (this can be a word, numbers, characters or a mix. Just start with 8). Every password will use this same base. Then add 2 words that are relevant to the site but aren't obvious (maybe the company founders name). Now bring your base back but reverse it and append a number, letter or character.
This (and any system you develop like it) will give you a password that is easy for you to remember, that is unique for every important site and damn near impossible to brute force.
Here is a fantastic comic from XKCD about passwords and entropy.
Massimus - "Trump already has democrat support."