What's the environment variable for the path to the desktop?

To be safe, you should use the proper APIs in Powershell (or VBScript)
Using PowerShell:

[Environment]::GetFolderPath("Desktop")

Copy something using Powershell:

Copy-Item $home\*.txt ([Environment]::GetFolderPath("Desktop"))

Here is a VBScript-example to get the desktop path:

dim WSHShell, desktop, pathstring, objFSO
set objFSO=CreateObject("Scripting.FileSystemObject")
Set WSHshell = CreateObject("WScript.Shell")
desktop = WSHShell.SpecialFolders("Desktop")
pathstring = objFSO.GetAbsolutePathName(desktop)
WScript.Echo pathstring

I found that the best solution is to use a vbscript together with the batch file.

Here is the batch file:

@ECHO OFF
FOR /F "usebackq delims=" %%i in (`cscript findDesktop.vbs`) DO SET DESKTOPDIR=%%i
ECHO %DESKTOPDIR%

Here is findDesktop.vbs file:

set WshShell = WScript.CreateObject("WScript.Shell")
strDesktop = WshShell.SpecialFolders("Desktop")
wscript.echo(strDesktop)

There may be other solutions but I personally find this one less hackish.

I tested this on an English PC and also a French PC - it seems to work (Windows XP).

EDIT: Use the accepted answer, this will not work if the default location isn't being used, for example: The user moved the desktop to another drive like D:\Desktop

At least on Windows XP, Vista and 7 you can use the "%UserProfile%\Desktop" safely.

Windows XP en-US it will expand to "C:\Documents and Settings\YourName\Desktop"
Windows XP pt-BR it will expand to "C:\Documents and Settings\YourName\Desktop"
Windows 7 en-US it will expand to "C:\Users\YourName\Desktop"
Windows 7 pt-BR it will expand to "C:\Usuarios\YourName\Desktop"

On XP you can't use this to others folders exept for Desktop My documents turning to Meus Documentos and Local Settings to Configuracoes locais Personaly I thinks this is a bad thing when projecting a OS.

KB's answer to use [Environment]::GetFolderPath("Desktop") is obviously the official Windows API for doing this.

However, if you're working interactively at the prompt, or just want something that works on your machine, the tilda (~) character refers to the current user's home folder. So ~/desktop is the user's desktop folder.

Not only would that not work for an International version of Windows, it would fail if the user had edited the Registry to make their Desktop folder reside somewhere else. You can query the Registry for the file location using the REG command:

REG QUERY "HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders" /v Desktop

To get this into a variable use something like this:

FOR /F "usebackq tokens=3 skip=4" %%i in (`REG QUERY "HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders" /v Desktop`) DO SET DESKTOPDIR=%%i
FOR /F "usebackq delims=" %%i in (`ECHO %DESKTOPDIR%`) DO SET DESKTOPDIR=%%i
ECHO %DESKTOPDIR%