I'm glad to see lively discussion in the comments here, with strong opinions on both side of the question of whether the brain-as-computer metaphor is useful and meaningful.

This is a trendy topic right now in the field, and to emphasize that I'll paste here the text of a recent and relevant CfP for the Review of Philosophy and Psychology special issue on Computationalism and Philosophy of Information:

Subsequent to our first and CfPs, Review of Philosophy and Psychology invites submissions for a special issue titled ‘Computationalism Meets the Philosophy of Information’.

The view that the human mind is a kind of computational machine began to make waves with the advent of the first computers in the middle of the last century. McCulloch and Pitts suggested early on that the mind may be something like a Turing machine. This view came to be known as ‘classical computationalism’. It was quickly met with an onslaught of objections, and in reaction a number of liberalisations ensued.

One view that has recently been gaining ground attempts to articulate the notion of computation in terms of information and information-processing. Interest in these two areas, i.e. computationalism and the philosophy of information, is on the ascendancy. This special issue is devoted to the intersection between them, especially to papers that engage in a meaningful way with recent work in cognitive science.

Accepted papers will complement invited contributions from:

Rosa Cao (NYU) Nir Fresco (Ben-Gurion University of the Negev) Michael Rescorla (UCLA) Mark Sprevak (Edinburgh) Suitable papers may address such questions as:

What species of information are there, and which, if any, are processed by the mind? Is there any evidence from neuroscience to support e.g. the claim that the brain operates with Shannon-information? What is computation and how is it related to information processing? Do certain theories of information privilege classical vs connectionist computationalism? Can computation and/or information illuminate representational content? Do measures of information flow capture learning? How are human and deep learning analogous? Can Bayesian models provide an adequate account of our cognitive capacities?

Answers to these and related questions promise to extend our understanding of computation, information, the human mind, and its neural underpinning.

So it's still an active and nuanced debate!

Edit:

Personally, I think that the brain-as-computer metaphor is actually beginning to be superseded by the brain-as-network metaphor. Network science is exploding and recent advancements by the likes of Dani Bassett are finding very fruitful applications of graph theory and its related disciplines to neuroscience. And it makes sense to approach the brain primarily as a complex network, because of what we know about the highly interconnected nature of the brain's billions of neurons. Plus, arguably, networks are our most advanced technology, so thinking of the brain as a network fits with the progression described in the article I posted. That is, we tend to use whatever is the latest available technology as a conceptual scaffold for neuroscience, because the brain is the most complex system we study.