I think it was in Visio 2007 a new feature called auto connect was added which adds blue triangles on the side of visio objects (Shown in image below) and if pressed will auto connect to some other object/shape. This can get quite furstrating as they are very easy to accidentally click.
To switch off this feature choose:
Visio -> Tools -> Options -> General Tab
Deselect the 'Enable AutoConnect' option