One plugin which I use frequently on my WordPress development projects is the Top Level Categories plugin. What this plugin will do is remove the /category/ from the URL upon activation. For example:

http://www.example.com/category/uncategorized/ will change to http://www.example.com/uncategorized/

No other configuration to the plugin is needed, all you need to do is activate. This plugin is best used in combination with a permalink structure like /%category%/%postname%/.