Let $\tilde h^\bullet$ be a reduced generalized cohomology theory, and let $T^2$ be the torus. For what theories $\tilde h^\bullet$ is $\tilde h^\bullet(T^2)$ known (or easily computable)?
$H_n(T^2) = \mathbb Z$ for $n=0,2$, $\mathbb Z \oplus \mathbb Z$ for $n=1$, and $0$ otherwise, so from the universal coefficient theorem we can get $\widetilde H^\bullet(T^2;A)$ for arbitrary coefficient $A$.
I believe for complex K-theory we have $\widetilde K^n(T^2) = \mathbb Z \oplus \mathbb Z$ for odd $n$ and $\mathbb Z$ for even $n$. It's not hard to find this on the web.
What are some other examples? I'm specifically looking for non-ordinary theories (e.g. cobordism, cohomotopy, etc.).