It is possible to remember an arbitrary number of different, safe passwords. My method is to have one password that is short, but hard, in the meaning of impossible to crack by dictionary attack. Think random letters, numbers, the stuff that is hard to memorize. But it's always the same base password, so you will know it by heart eventually. Assuming the website you use the password on hashes the password, that leaves you vulnerable to lookup/rainbow tables, because the base password should be fairly short, below 10 chars.
To defeat rainbow tables, I salt that password in a way I don't have to memorize but can easily deduce, for example with the site I'm using the password on. Examples: ReallyHardPasswordSlashdot, ReallyHardPasswordGoogle, ReallyHardPasswordSteam, etc. They all are different and not reusable, their hashes are different, they are (hopefully) long enough to be too long for rainbow tables