Is there a "light version" IntelliJ IDEA to edit files WITHOUT a project?

Since IntelliJ IDEA 2020.1, there is LightEdit Mode. It's really light :)

LightEdit mode lets you use IntelliJ IDEA’s text editing features without creating or opening a dedicated project. In LightEdit mode, a file is opened in a separate editor window which may coexist with other (project) windows.

The mode has certain limitations: it offers simpler code completion (or sometimes none at all), no code inspections, only basic code highlighting that doesn’t require sophisticated code analysis, and so on. But if you just need to open a single file, make a few changes, and save, LightEdit is the quickest way to do it, and you don’t have to use a third-party editor either.

UPDATE: It's now supported using the LightEdit mode.

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Original answer:

It's not possible at the moment, there is a related request (created 11 Dec 2010), you can vote for:

• IDEABKL-5939 using IDEA as a general-purpose text editor