Why do universities have to spend money on journals?

This is a really big question, which unfortunately has no simple answer. Some short comments:

Universities have very little choice about subscribing to journals, as long they publish good papers, since faculty need access to those papers to do their research. The solution has to start on the publishing side.

Collaborating to create free, open access, peer-reviewed journals is a fine idea, but either you need to convince universities to support this financially, or you need to recruit enormous numbers of dedicated volunteers. (Whenever this topic comes up, someone is sure to point out that volunteers run some free, high-quality online journals. Of course they do, but the question is how to recruit hundreds of times as many volunteers.)

Printing is a non-issue. Everything is already available online, with printed copies only for those who want them.

In a mathematics context, see http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf and http://arxiv.org/abs/1204.1351 for more details.

My take on parts of your question:

Currently we do have an arXiv, maintained by academia and where researchers regularly upload parts of their work.

I may be on something of a crusade against arXiv users who believe arXiv is more than it is, more more widely adopted than it is. "We" don't have arXiv - certain disciplines have it. Other disciplines, equally valid as those which support arXiv, both don't use it and have understandable issues with the reliance on a pre-print site as a way to disseminate findings.

Why do universities splurge lots of money to publish in third-party journals? The question especially applies to journals that operate with a rigorous profit motive.

First, they're not paying money to publish in the journals. They're paying money to be able to read said journals. I've published in for-profit journals, even ones my university didn't subscribe to, for free.

The subscription is very high, so wouldn't publishing in such journals affect the paper's citation count and deter the spread of knowledge about the work within academic circles?

Not necessarily. Papers are often available from the author, inter-library loans, etc. Beyond that, how a paper gets cited is a far more complex question than just "Do you have to pay for a subscription", and I don't think Open Access journals have compellingly showed that the citation counts are higher for open journals. The readership and downloads? Probably, but in terms of citation the Open Access journals are still struggling with a perceived gap between their prestige and the prestige of the "leading" for-profit journals. Perhaps that will change in time, but there are ways to get journal articles that your institution doesn't subscribe to, and those ways are often fairly trivial.

Why should not universities collaborate to create free, open access, peer-reviewed journals?

Some do - but for many the cost of laying out and producing a twice monthly journal would be distracting from the core mission of the university (or more likely, particular departments), and they'd run into staffing and budget concerns. Most don't have the money to fund what they actually need to do, let alone add a publishing arm that may or may not ever make money.

And those groups that are interested, like professional societies and the occasional university? They often turn to for-profit publishers to outsource it. For example Epidemiology, a publication of The International Society for Environmental Epidemiology is published by Lippincott. The American Journal of Epidemiology, which is put out by Johns Hopkins and sponsored by the Society for Epidemiologic Research? Published by Oxford.

Moreover, given the need to conserve paper, why should journals spend on printing research papers? Wouldn't an online version suffice, as most people use only local computer printouts anyway?

Because some readers want the paper versions. Seriously, nearly every journal I know has an "online only" subscription for less money. But if you want a paper version, why shouldn't you be able to get it?

Nothing actually comes for free. Expensive journals tend to have established their merit with a long history, and managing / maintaining that quality across decades and editors has traditionally been the job of publishers. Why?

Although publishing can be a pain, but it is absolutely key to academic progress. We need to be able to rank contributions if for no other reason than to determine what to spend our precious time reading. Like all systems with power, publication is potentially subject to corruption. Publishers are traditionally seen as more objective than authors or universities, since their reputation and income is entirely determined by how good a job they do of publishing selectively.

You could imagine a situation where a bunch of universities got together, dedicated their resources (paid their staff's time) to make an objective publishing system that was not controlled by any one academic institution. But that is actually what most academic publishers are. In fact, many academic publishers are associated with individual universities.

The problem remains, who pays? Currently, in general readers / consumers pay, and they probably are really in the best place to know whether research is worth purchasing. But under open access, the authors pay. This can actually be immensely more expensive for universities than paying subscriptions, since they produce a lot of research. For example, my university spends less than the cost of two PLoS open-access articles per year per academic on subscriptions, but most academics are expected to publish a lot more than two articles a year. The other problem with authors paying is that there is then a moral hazard. Journals are effectively bribed to take papers, which may result in compromising the selective process that underlies academic progress. This would be a terrible cost.

Many academics self-publish by putting their papers on line or just writing blogs. This can be effective, but note that it returns to the problem of knowing what is worth reading. Generally, successful academic blogs are run by people who also prove themselves as academics by publishing in highly-rated journals, so this is not really an independent solution.

The short answer then is: because paying to read publications is the best system we currently know.