Can the snapping function be turned off for the Measure Tool in ArcGIS Desktop 10?

Yes. The Snapping toolbar must be displayed in order to turn off snapping. If there is heavy data or many data layers displayed in ArcMap, automatic snapping severely interferes with the ability to measure distances.

Turn off the snapping function from the Measure Tool by displaying the Snapping toolbar and unchecking Use Snapping from the Snapping drop-down menu.