Jigsaw puzzle: isolating the pieces (separating "stuck" blobs)
I agree with Abid Rahman K, however eroding only would result in shape shrinkage.  To only get rid of the gap, Abid Rahman suggests a watershed based approach, but for a faster and easier method you might try:


Erode the regions
Apply connected component labeling.
Dilate the regions back.


This way you will have almost the same shape (with some artifacts arising due to morphology) but you will surely end up with single connected components. 

Watersheds and distance transform are also powerful and might be good choices if you have a lot of overlap.