We've recently had a few questions regarding the legal aspects of using ArcGIS Explorer screen shots in educational materials and publications. ArcGIS Explorer's default content, and the content found on the Resource Center, are published via ArcGIS Online. The ArcGIS Online FAQs cover the use of this content.

In short, yes, you can use Explorer screen shots if you're not using them for commercial purposes, provided you include the required attribution. When you choose View > Copy View to Clipboard, or use File > Print, you automatically capture the required attribution in the lower middle of the screen.