Is there any publication venue that makes rejected papers available for download?
I am most interested in the field of computer science, and English-speaking venues.
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I do not know of any, and I can't imagine any that would. Typically, the journal would not have the copyright assignment until after they accepted, though I hear that some venues ask for this upfront. Additionally, this isn't really how academic publication is supposed to work. A rejection isn't the end of the road for a work of scientific authorship. Many works are published elsewhere after being rejected. This would kill that process.
(Preprints notwithstanding, for works in fields where preprints don't count as publication.)
At Vixra.org you will find papers often rejected from Arxiv.org, and possibly also from the 'printed' press.
As Bill Barth said, I don't believe anyone identifies or distributes rejected papers. However, you might be able to get private access if you are interested in doing statistical analysis. Of course no journal or conference would let you publish anything identifiable about specific rejected papers, they wouldn't let you access their data at all without some legal paperwork and promises of confidentiality, and they might not even let you do the analysis yourself (instead, they could answer statistical queries for you, so you never got your hands on all the data). However, if you propose an interesting project regarding what distinguishes accepted from rejected papers, then they might be willing to work with you to collect some statistics. It's by no means guaranteed, but it can't hurt to ask if you have a project you are excited about.
If you mean a place where people can post rejected papers, any place you can post preprints, such as the arXiv or a personal webpage, will fill this role.
If you mean a journal that will publish rejected papers, normally people try to publish them in another journal, though after some difficulty, they may give up and leave them in the preprint form. There was an attempt to make a journal specifically for such papers in math, Rejecta Mathematica (this was a serious effort, with peer review), but foundered after a few years from lack of interest.
If you mean a journal that publishes submissions which are rejected (say publishes online papers which are rejected from a printed journal), one would need to get permission from the authors, who are not likely to be willing to give it. Also, if a journal publishes all papers they "accept" and all papers they "reject", they are just publishing all papers submitted and may as well not be a peer-review journal.
Actually there is one.
Copernicus Publications is an open access publisher that has some journals with an "open review model". Each paper in these paper has its full review process open for viewing to everyone. Each journal is actually two journals. The "regular" one and the "discussions" one, where it's possible to view the original submission, any revisions, reviewers comments and author replies. People who are not the assigned reviewers can also post comments on papers under review.
You can view this for both accepted and rejected papers, which is nice because then you can compare and see what makes one paper strong and another one weak.
Not much computer science in there, but it has some areas which may be tangentially related in the "Math|Data|Informatics" section: http://publications.copernicus.org/open-access_journals/math_data_informatics.html
There is the Journal of unsolved Questions JunQ. They collect ‘null’-result research and open problems. This may include previously rejected work.