Invented the first plates?
either Greeks or egyptions
According to the various sources brought in the Answers.com page at http://www.answers.com/topic/license-plate there is some debate as to who was actually the first to institute license plates. It appears that the Netherlands were the first to introduce a plate in 1898. New York has been requiring plates since 1901, but they didn't issue standard plates. The first States to issue standard plates were Massachusetts and West Virginia in 1903.
Paper plates were invented mostly because it's handy. On picnics, on the go, and traveling, nobody has the space, protection, and time for china plates to be carried around. Plus if you're sick or feeling off and you use paper containers for your meal, you only have silverware and maybe a cup to wash; throw the napkin and plate away and say good riddance!