Update: It turns out WordPress.org saw an increase in database load issues due to experimental changes. For now the changes have been rolled back, fixing this. (Speaking of changes, check this out.)
Earlier this morning reports began popping up about an error showing up in WordPress Dashboards. New plugin or theme searches via the dashboard were reporting back: “An Unexpected HTTP Error occurred during the API request”, temporarily breaking searches. It seems the API request is timing out before a connection is made, which is likely an issue at WordPress.org.
The issue affects many WordPress users, as far as we can tell. Mentions of it have popped up in the support forums, but not in large numbers. According to that particular linked thread, increasing the API timeout length will sidestep the problem, but we don’t recommend editing core files for any purpose. There’s no reason not to think this issue is a temporary one that will be cleared up soon.
Themes and plugins can, of course, still be installed and activated by uploading them from the dashboard or via FTP. Since WordPress.org/extend is still working properly you shouldn’t have any issue finding a theme or plugin and downloading it directly.
We’ve reached out to the folks behind WordPress.org to find out more about the issue, and will update this post when there’s more to tell.