Instead of using the Type > Insert White Space > Nonbreaking Space character, highlight a regular space and apply "No Break" from the flyout menu of the Character palette (or flyout menu from Control panel when in Character mode).

-- K.

In InDesign CS 3 we added support for a character to represent non-stretching non-breaking spaces because the original implementation (non-breaking spaces don't stretch) was incorrect. The option is in the same Type > menu:
* Non-breaking space - u00A0 (NO-BREAK SPACE)
* Non-breaking, non-stretching space - u202F (NARROW NO-BREAK SPACE)
We didn't strecth u00A0 in the beginning because the work-around that Kent describes was considered workable. However, especially in the Czech & Polish market, this method of applying the no-break attribute didn't fit well into the workflow of importing external documents because around 10-20% of the spaces needed to be this type. The CE version of InDesign had changed the non-breaking space (u00A0) behavior for these languages.
When converting an earlier document we replace u00A0 with u202F to preserve the original behavior.

Great news!

Thanks a lot