What's wrong with this MySQL query?

You are using the wrong quotes. Use ` instead of '

CREATE TABLE `topics` (
  `topicid` int(11) unsigned NOT NULL AUTO_INCREMENT PRIMARY KEY,
  `creator` varchar(255) NOT NULL,
  `createtime` datetime NOT NULL,
  `content` text NOT NULL
) ENGINE=InnoDB;

I also would recommend specifying the engine.

The error is the single quotes around the table and column names. If you want to escape these names use back ticks (`) not quotes.