Answer: (C)
Solution: A square has no acute angles among its four interior angles, so (A) is incorrect;
An obtuse triangle has only one obtuse angle, so (B) is incorrect;
If a polygon has more than three acute angles, then the exterior angles of these angles are all obtuse, and the sum of more than three obtuse angles would exceed $360^{\circ}$, which contradicts the fact that the sum of the exterior angles of a polygon is $360^{\circ}$. Additionally, a quadrilateral with four interior angles of $89^{\circ}, 89^{\circ}, 89^{\circ}, 93^{\circ}$ can be found, so the interior angles of a convex polygon can have at most three acute angles, hence (C) is correct;

A regular hexagon has six obtuse angles, so (D) is incorrect.
Therefore, the correct choice is (C).