Two vertices snap together when snapping during transform is enabled with snap onto self :
How could both vertices be merged?
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AutoMerge Editing might be what you are looking for. It can be toggled on and off by clicking the entry.
EDIT: I've added the image posted as a comment by username: gandalf3 since he pointed out that there is also toggle button in the header bar which makes this feature easier to access.
Update for blender 2.8 OSX (in addition to Meetai.com's comment)
AutoMerge Editing can be found