Maybe the rcrossref package for R is helpful. To find the number of citations, You can do things such as
# returns list:
# pap <- cr_works(dois = "10.1371/journal.pone.0042793")
# pap$data will be 28-column data frame.
cr_citation_count(doi = "10.1371/journal.pone.0042793")
Pubmed has data about 23 million biology and medicine papers. Unfortunately I think you need to request access and given US politics at the moment it could take some time till there a human available to give you that access.
PubMed Central changed all adressess and some methods.
To bulk access you can use complex FTP procedures similar to the described below in the "OLD" section... Or a simple perl (or shell) script to loop over API.
The basic GET API are showed at https://www.ncbi.nlm.nih.gov/pmc/tools/get-full-text/
To GET by shell you must to use ...
To update Cristian's answer, with regard to PubMed, you don't need to be from the USA. There are a couple of ways to get the data.
1) PubMed, go to http://www.ncbi.nlm.nih.gov/pubmed/?term=%22all%22%5Bfilter%5D (which today hosts 25M articles - not OpenAccess) choose send to -> file -> abstract or xml. I downloaded the XML which is kind of larger - 298.298....
For papers on computational linguistics, there is an archive of 24,300 papers at http://aclweb.org/anthology/ , with an active community interested in better retrieving this data such as DFKI and DERI.
For anyone still looking for sources of citation network data, and paper metadata for global cross-disciplinary publications, the Open Academic Graph project from Microsoft and AMiner combines two of the largest indexes, and is free.
If you are interested in downloading full content (i.e. PDF/LaTeX source), then arXiv will ...
Although for papers in economics alone, RePEc has several advantages for your project:
Data is free: http://repec.org/docs/RePEcDataUse.html
Full FTP access to the structured data
Multiple metrics for authors
Broad data coverage
I am not sure that you can get everything you are looking for directly, but here are a few sites that have some of the information you're looking for:
Cite Seer: http://citeseerx.ist.psu.edu/
Social Science Research Network: http://www.ssrn.com/
Google Scholar: https://scholar.google.com/
Note that the 'free' and 'open' -ness of these sites should be ...