Offhand, it is hard to think of a function that does not have even a one-sided limit. This video shows one!
One-Sided Limit that Does Not Exist
Offhand, it is hard to think of a function that does not have even a one-sided limit. This video shows one!
Mathtuition88 
Many thanks ! BTW, I think these examples and other beautiful examples are mentioned in Calculus and Analytic Geometry of Thomas and Finney.
Also, it would be great if you could post more such videos on conceptual calculus/analysis !!!
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Sure, I will post these as I encounter them! Such videos are a rare gem.
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