Is there an analog of PhotoShop's "Magic Wand Tool" in ArcGIS Desktop?

I don't think you'll get a tool that does exactly what you've described... Something similar, but maybe not as diverse in its use, could be the Grid Editor from a Dutch company called ARIS. http://www.aris.nl --> GridEditor

It's able to easily change the raster values of selected cells. Also, it's able to do this (quote from website):

• change the value/color of a zone of cells with identical values (paintcan)
• replace one value with another value in the entire grid (value replacer)

So I guess this is pretty close to what you try to find. Now to the downside of the tool: I've only ever tried the free trial version, which is quite limited in use. For the full version you need to pay. Licenses are permanent but they cost like 390 $...

TerraAmazon offers a magic wand tool. Unfortunately it requires that you setup a postgis server first.

The ArcScan extension docs talk about a tool named Magic Erase which sounds like it is more interactive than Photoshop's magic wand but still useful:

• Click an erase tool on the Raster Painting toolbar. [...] You can change the brush size with the Erase Size button Erase Size.
• Click the Magic Erase tool Magic Erase. [...] Drag the tool over the raster cells to erase them. When using the Magic Erase tool, connected cells are erased, although any connected cells that extended beyond the dragged box are not erased.

Also perhaps of interest is the QGIS Magic Wand plugin by @Kanahiro. It creates a polygon by analysing the map canvas. There are settings for threshold and accuracy, and they suggest adjusting saturation for better results.