Rectangular parallelepiped/prism (a box)
with length $a$, width $b$, height $c$
$$V=abc$$
$$I_{xx}=\frac{1}{12}m(b^2+c^2)$$ $$I_{yy}=\frac{1}{12}m(a^2+c^2)$$ $$I_{zz}=\frac{1}{12}m(a^2+b^2)$$
$$I_{xy}=I_{yz}=I_{zx}=0$$
Solid Cylinder
with radius $r$ and length $h$
$$V=\pi r^2 h$$
$$I_{xx}=I_{yy}=\frac{1}{12}m(3r^2+h^2)$$ $$I_{zz}=\frac{1}{2}m(r^2)$$ $$I_{xy}=I_{yz}=I_{zx}=0$$
Thick-walled cylinder
with inner radius $r_i$ and outer radius $r_o$ and length $h$
$$V=\pi (r_o^2-r_i^2) h$$
$$I_{xx}=I_{yy}=\frac{1}{12}m(3(r_o^2+r_i^2)+h^2)$$ $$I_{zz}=\frac{1}{2}m(r_o^2+r_i^2)$$ $$I_{xy}=I_{yz}=I_{zx}=0$$
Thin-walled cylinder
with radius $r$ and length $h$
$$I_{xx}=I_{yy}=\frac{1}{12}m(6r^2+h^2)$$ $$I_{zz}=m(r^2)$$ $$I_{xy}=I_{yz}=I_{zx}=0$$
Solid Sphere
with radius $r$
$$V=\frac{4}{3}\pi r^3$$
$$I_{xx}=I_{yy}=I_{zz}=\frac{2}{5}mr^2$$ $$I_{xy}=I_{yz}=I_{zx}=0$$
Thin Hollow Sphere
with radius $r$
$$I_{xx}=I_{yy}=I_{zz}=\frac{2}{3}mr^2$$ $$I_{xy}=I_{yz}=I_{zx}=0$$
Solid Ellipsoid
with axis lengths $a$, $b$, and $c$
$$V=\frac{4}{3}\pi abc $$
$$I_{xx}=\frac{1}{5}m(b^2+c^2)$$ $$I_{yy}=\frac{1}{5}m(a^2+c^2)$$ $$I_{zz}=\frac{1}{5}m(a^2+b^2)$$
$$I_{xy}=I_{yz}=I_{zx}=0$$
Thin Hollow Ellipsoid
with axis lengths $a$, $b$, and $c$
$$I_{xx}=\frac{1}{3}m(b^2+c^2)$$ $$I_{yy}=\frac{1}{3}m(a^2+c^2)$$ $$I_{zz}=\frac{1}{3}m(a^2+b^2)$$
$$I_{xy}=I_{yz}=I_{zx}=0$$