When I blink, I see a black spot in the corner of my left eye. Should I be worried?

Floater. If the black spot moves with blinks, then it's likely in the vitreous. If not new and only one without flashes or decreased vision, may not be anything serious. If it's a fixed black spot, then should be checked out for a potential retinal or brain problem.
Maybe. This may signifiy a problem with the retina. When you blink it stresses the retina with rapid changes in light intensity and may uncover a weaker spot. Should be looked at with a dilated examination by an ophthalmologist.