I searched the forum and found a couple of discussions regarding the subject in 2009. It's 2012 and I have the same request (see attached). I haven't found a setting in the dim style or the RMB options to turn off the extension line. I saw the posts showing drawing a sketch in the view but come on, all that to just turn off the line?
IV 2012 all sp & fixes
What happens if you rotate the diameter dimensin around. Does the extention shorten and almost disapear?
I just submitted this to the Autodesk product comment site (otherwise known as the wishlist). I'd encourage others to do the same. I asked for the ability to control visibility and attachment point of diameter dimension extension arcs.
A good workaround is to
1) Sketch a circle on the view and constrain it.
2) Close the sketch
3) Dimension the circle.
4) Open the sketch
5) Select the circle and set as "sketch only"
But a programmed solution would definitely be better.