For Android devices, there's also MIT App Inventor, which is a very scratch-like environment for writing mobile apps, available here:

http://appinventor.mit.edu

In addition to basic I/O and animations, it's able to deal with a lot of the device capabilities, including SMS, GPS, dealing with the camera, and so forth.

Unfortunately, I don't know of any similar environment for programming iThings --- Apple fairly famously rejected a Scratch port from the app store in 2010:

http://wiki.scratch.mit.edu/wiki/Scratch_Viewer

although a "Scratch player" for Android is in alpha, and apparently, people are also working on pure HTML versions.

http://learn.code.org uses the same [Blockly?] interface, just tried the first few stages with my 4 year old this last week. Only problem was his general literacy; but he sat on my lap and did the thinking for the problems and I read out the text. Have used Scratch (and light-bot and various turtles) before too with an older child.

learn.code.org has quite a few interesting facets, including using Angry Birds and Plants vs. Zombies artwork; they also integrate light-bot as one of the avenues for learning.

There's also Blockly [0], which you can use to build similar software.

[0]: https://code.google.com/p/blockly/

I'll second this. Install Scratch, then stand back and let the child lead.

Wow that's great. Thanks for the tip. I'm going to check it out.