Rademacher complexity and lowerbounds in learning theory Is there any function class known whose Rademacher complexity has a non-trivial lowerbound? 
Can the Rademacher complexity be used to lowerbound the generalization error in any learning situation?
First, let's distinguish between empirical end expected Rademacher complexities. The former is defined for a function class $F$ and sequence of points $X_1,\ldots, X_n$, by
$$ \hat R_n(F;X_1,\ldots,X_n) = E_\sigma \sup_{f\in F}\frac1n\sum_{i=1}^n
\sigma_i f(X_i).$$
The latter is defined for a function class $F$ and distribution $D$, by
$$ R_n(F;D) = E_{(X_1,\ldots,X_n)\sim D^n}[\hat R_n(F;X_1,\ldots,X_n)].
$$

It's known that for any function class with VC-dimension $d$, we have
$\hat R_n(F;X)=O(\sqrt{d/n})$ (for any sequence $X$) -- and hence the bound carries over to $R_n(F;D)$ for all distributions $D$.

It's also known that the Rademacher complexity upper bounds the generalization error for agnostic PAC (plus a confidence term decaying as $\sqrt{\log(1/\delta)/n}$). On the other hand there exist adversarial distributions that force any learner to have a generalization error of $\Omega(\sqrt{d/n})$;
see, e.g., my course notes
https://www.cs.bgu.ac.il/~asml162/Class_Material
.

From these considerations alone, we can conclude that for any function class with VC-dimension $d$, there is a distribution for which $R_n(F;D)=\Omega(\sqrt{d/n})$. 

Edit: I also like to give the following exercise. Let $F$ be the set of all $\{\pm1\}$-valued functions on the integers. Prove that there exists a sequence of distributions $D_n$ such that $\lim_{n\to\infty}R_n(F;D_n)=1$.