Indefinite systems of matrices appear for example in the discretization of saddle point problems by mixed finite elements. The system matrix can then be put in the form
$$\begin{pmatrix} A & B^t \\ B & C\end{pmatrix}$$
where $A$ is negative (semi)-definite, $C$ is positive (semi-) definite and $B$ is arbitrary. Of course, depending on convention you may use definiteness conditions, but this is pretty much the structure of those matrices.
For these methods, Uzawa's method can be employed, which is actually just a "trick" to transform the system into an equivalent semi-definite system that can be solved by Conjugate Gradient, Gradient Descent and the like.
I face an indefinite system which does not have such a block structure. Uzawa-type methods do not apply in that case. I am aware of the Minimal Residual method (MINRES) that has been introduced by Paige & Saunders, which is just a three-term recursion and seems to be easy to implement.
Question: Is MINRES generally a good choice, say, for prototyping? Is it of any practical relevance? Preconditioning is no central issue at the moment.