The thickness of an eggshell depends on what animal's egg you are talking about. The usual chicken eggs we eat at home is about 0.3mm thick.

Most animals who lay eggs have an outer protective layer but not a hard "shell". Other animals who have eggs, like amphibians have a thin layer. Also, the texture of an egg varies between animals. Snake eggs are more leathery whereas fish eggs are slimier and chicken eggs are harder on the outside.

An ostrich lays of one of the largest eggs of any animal and is the strongest. They measure about 0.06 inches in thickness and can way about 3.1 lbs.