What shapes are able to be tiled?

Answer 1

Squares or rectangles.

Answer:

Shapes which can be tiled (fit together without spaces or overlaps) are said to exhibit tessellation. These can be as simple as two dimensional shapes (squares and triangles) or as complex as the drawings by M.C. Escher who made tiles of birds and fishes.

In general tiling shapes can be regular polygons (all the same) or mixtures of different shapes of regular polygons. More exotic shapes are developed by mathematicians. These include tiles using irregular polygons and three dimensional shapes.