How can I disable automatically joining the General chat when I log in?

After significant investigation, the only option right now is to leave the channel when you log in, to do this type

/leave

Leaving the channel will persist in patch 1.03.

Please note that we will also be making a change with patch 1.0.3 so that if you leave General chat once, the game will remember this preference and you will not automatically join General chat again when logging in. While we don't yet have a date to share for this patch, we anticipate that it will be released before the end of the month.

This does not exist yet, but Blizzard has stated that they plan on adding it in a future patch:

We're looking to add functionality in a future patch that will "remember" if you've left General chat. It'll work similarly to World of Warcraft -- after you've left General chat once, you won't be automatically re-added to the channel whenever you next log in. It will essentially "opt you out" of the channel, but you'll still be able to re-join it manually.

In the meantime, you will have to use /leave each time you join in (but not before reporting all the gold-selling spammers first, right?).

I haven't found a way to automatically not join, but you can either click on the uppermost icon next to the chat area (looks like a gear, titled Public Chat Options) and select "Leave Channel" or type /leave.