No Lambda Normal Form
If a term has a normal form then there is a sequence of $\beta$-reductions leading to it. However, $\Omega$ has only one $\beta$-redex, which leads back to $\Omega$. Therefore, because $\Omega$ is not already in normal form it has no normal form.

It is easy to generate other terms that have only infinite chains of reductions. For instance, the related $Y$ combinator $Y = \lambda f . (\lambda x . (f (x x)) (\lambda x . (f (x x))$ gives
$$Y \to \lambda f . f Y \to \lambda f . f(f Y) \to \lambda f . f(f(f Y)) \to \cdots$$
Note that by applying $Y$ to a specific $f$ we may get a normalizing term (because for a specific $f$ there will be additional reductions that may lead to a normal form). In fact, $Y$ is quite useful because for any term $g$ we have $Y g = g (Y g)$, so $Y$ computes fixed points.