This is a list of text editing and word processing applications that natively support the Unicode standard, some of which may be useful for developing Unicode art.  If you know of an application that supports Unicode correctly but is not listed here, we'd like to know so we may add it to this list.

Corel WordPerfect
http://www.wordperfect.com/

WordPerfect is the world's longest-running full-featured word processing application, which, after being owned by computer networking pioneer Novell, Inc. (whose networking products also include Unicode support), was eventually purchased by a Canadian company called Corel.  WordPerfect continues to improve and evolve, evidenced by the addition of Unicode support in versions 10 (requires Service Pack 4), 11, and 12, and the built-in functionality to publish directly to industry-standard PDFs (a global Unicode-friendly standard format that was created and popularized by Adobe).

Durdraw (by Sam Foster)
https://www.durdraw.org/

Versatile ASCII and ANSI Art text editor for drawing in the Linux/Unix/macOS terminal, with animation, 256 and 16 colors, Unicode and CP437, and customizable themes.

See also:  https://www.github.com/cmang/durdraw (source code)

OpenOffice.org
http://www.openoffice.org/

OpenOffice.org is an open source word processing application suite with native Unicode support.  Compatible with all other major office suites, the product is free to download, use, and distribute.

SC UniPad - The Unicode Text Editor
http://www.unipad.org/

SC UniPad is a Unicode plain text editor for the Windows 9x/ME/NT/2000/XP operating systems.  One of its big advantages is that it can display more than 53000 Unicode characters without installing extra fonts.  It's free for documents smaller than 1k.

UniRed
http://www.esperanto.mv.ru/UniRed/

A free, open source Unicode plain text editor for Windows 95/98/NT/2000.