
Remember, the free version of these sites is best-suited for testing purposes. If you're planning for a full-fledged development instance, go for the premium version as they don't expire, automatically.
Although these test WordPress instances are quite safe to use, I'll still strongly advise avoiding using any sensitive information within the plugin settings or in the posts and pages. Let's check out our options.
Free WordPress Test/Sandbox Site - WPSandbox.net
This is my preferred service to quickly create a sandbox instance for testing WordPress plugins. It's quick, reliable with a no-nonsense interface.It's not just WordPress, but one can also create ClassicPress instances through this service. Both new and old versions of WordPress are supported by this service.

Power users can also enable SFTP access to work directly on the files. The debug option lets developers get vital data during the testing phase. One can also access the database through the web interface. And, if you want a multi-site instance, this service has that too.
Although one can install both the plugins and themes from the dashboard, the service facilitates the installation of both (in advance) while creating the test instance.
WP - Sandbox
Another good option to launch test sites with WordPress is WP-Sandbox. It has a very simple interface that enables you to spin up a sandbox WordPress instance without any hiccups.One of the differences between the former and this service is that the former one doesn't force you to first create an account to build a test website. This one requires you to first create an account before creating a test site.

You get a generous 1GB space for your site which is more than good for testing themes and plugins. There's no restriction on plugins and themes. You can even reset your test installation to start from scratch after experimenting.
If you want to export your content and data, there's no restriction on that too. I often use this service for testing small changes to a custom design. The export feature lets me make the changes to a different website.