Eric Weisstein, MathWorld: Dimension = A topological measure of the size of an object's covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the object.
American Heritage Dictionary: Dimension = The least number of independent coordinates required to specify uniquely the points in a space.
Webster's Revised Unabridged Dictionary: Dimension = The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.