How do I add custom styles/plugins to the rich text editor in Craft? I'm aware that I can customise which buttons is available in the rich text editor. But how can I add custom css styles, either as classes or as inline styles? Do I need to create a plugin for this? If so, how do I add plugins? And, can I change which options are available in the formatting drop down?
If by styles you mean the formatting drop-down, just add them in an array:

{
    buttons: ['bold', 'italic'],
    formatting: ['p', 'blockquote', 'h2', 'h3', 'h4', 'SomeHtmlTag']
}


.

If you want to have a button which adds custom CSS-classes, take a look at: Redactor CSS by Nathan Doyle



Update (July 2015)

Craft 2.3.2615 (Dec 2, 2014) and above use Redactor 10, which includes the formattingAdd setting for adding custom styles and classes.

formattingAdd: [
{
    tag: 'p',
    title: 'Red Block',
    class: 'red'
}