Desktop Calendar is a free tool which displays an editable calendar on your desktop.

After installation, a full month view calendar is displayed on your desktop, then switched to other months or years in a click or two.

That's sort-of useful all by itself, although you do need to keep in mind that the calendar is displayed instead of your desktop icons, not as well (a Win+D hotkey switches from one to the other).

Double-clicking any day enables entering a text note, appointment, reminder, whatever you like. There's nothing advanced, no scheduling or reminder system, the only other option is to assign a background colour for a particular day.

An administrative menu has some extra tools, including importing and exporting calendars to the program's own format, printing them, or customising the calendar display to suit your needs.

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It can be convenient to display your calendar on the desktop, but Desktop Calendar's lack of scheduling or reminder tools, and the way it hides your desktop icons, mean it won't be the best solution for everyone.