There is no good health reason to remove the vein from fresh shrimp. Contrary to what you may have heard, the vein's color comes from the sediment on which the shrimp feeds: it is not a concentrated source of contaminants, according to Tim Fitzgerald, Senior Policy Analyst at the Environmental Defense Fund.
However, many people find it unsightly, and removing it is an aesthetic decision. In very large shrimp, the veins tend to be more visually prominent and may also contain bits of gritty sand: in that case they should certainly be removed.
When you can't see the vein in raw shrimp, it rarely makes sense to go digging around looking for it. When the vein is thick (or visible beyond your liking), remove it by running the tip of your knife down the center of the back. Watch our video on Peeling and Deveining Shrimp.