How to show the ‘Recent Posts’ in the sidebar?

One way:

https://www.coffee2code.com/archives/2004/08/27/plugin-customizable-post-listings/

Can you do this without a plugin?

The plugin method — I would hazard an educated guess and say — is probably by far the easiest way to do it. Drop in the plugin, activate it, and add the appropriate code to your sidebar: job’s a good ‘un!

Looks like a useful plugin.

Gareth

Can you do this without a plugin?

Yes. It requires advanced usage of The Loop.

But a plugin is not theme dependent, and you can turn them off for troubleshooting or if you change your mind.