The force that tends to make objects spherical is gravity. In the absence of gravity, there is no preference for shapes, so objects will be in any shape. Larger bodies exert more gravity, and so tend more to be round.

Neutron stars, short of black holes, are the most strongly gravitationally bound objects in the universe. In black holes, all of the mass is contained in a single point with no volume. Thus, neutron stars, which still have finite volume, are also the most perfectly spherical objects in the universe.

Most astronomers think that asteroids are failed planets, which is to say that they are leftover rock from the birth of the solar system that never stuck together to form into planets. While the question of irregular shapes can be answered in various ways (with various levels of scientific jargon), the basic reason is that the asteroids are too small(most are under 200km) for gravity to be able to deform them into spherical shapes. The strength of the rock is stronger than the strength of gravity.

Actually, saying that asteroids are too "small" may not be the right way to phrase it, since this also depends on density. Neutron stars are often only about 20km in diameter, but have a mass of almost 1.5 times the mass of the Sun. (They are the densest known objects, in fact.) Because neutron stars are such extremely massive objects,compressed to such a high density and bound by a gravitational force,they would be round in the absence of rotation.