Sometimes, given an object A in an Abelian category, the Yoneda product on Ext(A, A) is gradedcommutative, for example in cases where it coincides with the cupproduct in singular cohomology. Are there any nice theorems about when the Yoneda product is gradedcommutative in general? Thanks in advance.

I move this to a more proper answer to discuss some subtle points of the question. The EckmanHilton argument (or more concrete calculations) shows, as Chris points out, that $\mathrm{Ext}(A,A)$ is commutative when $A$ is the unit for a monoidal category. The subtleties appear when we consider for instance the ring $R=k[x]/(x^2)$ for $k$ a field and $A=k$. Then $A$ has a uniform resolution $\dots\xrightarrow{x}R\xrightarrow{x}R\xrightarrow{x}R\to k\to 0$ giving $\mathrm{Ext}^i(A,A)=k$ for all $i$. Using the definition of the Yoneda product in terms of maps of resolutions we get that $\mathrm{Ext}(A,A)$ is the polynomial ring on $\mathrm{Ext}^1(A,A)$. This is graded commutative only when the characteristic is $2$ (and then it is not graded commutative in the strict sense of the square of odd degree elements being zero). However, it is exactly in characteristic $2$ that $R$ is the affine algebra of a finite group scheme (with $x\mapsto x\otimes1+1\otimes x$ as coproduct) with $k$ the unit for the associated monoidal structure on the category of $R$modules. Hence we have a monoidal reason for the $\mathrm{Ext}$algebra being graded commutative in characteristic. On the other hand we have a uniform description of the $\mathrm{Ext}$algebra in all characteristics which just happens to fulfil the definition of being graded commutative in characteristic $2$. 


Another starting point is to think of ${\rm Ext}(A,A)$ as the derived endomorphism ring of the object $A$ and recall Schur's lemma. If $A$ is a finitelygenerated simple module over a ring $R$, then ${\rm Hom}_R(A,A)$ is a division algebra. For example, if $R$ is a $k$algebra over an algebraically closed field $k$, then ${\rm Hom}_R(A,A)$ is isomorphic to $k$ (so, in particular, it is commutative.) Via FreydMitchell embedding, this should give some idea what to expect in degree $0$. Going back the question, then, the examples one might have in mind are categories of modules over a group ring or enveloping algebra of a graded Lie algebra: in these cases, ${\rm Ext}(k,k)$ is group or Lie algebra cohomology, respectively, and has a gradedcommutative cup product, where $k$ is the trivial module. Perhaps there is a suitable "semisimplicity" hypothesis one could impose on the category so that ${\rm Ext}(A,A)$ is gradedcommutative for all simple objects $A$? 

