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Many probabilists are already using the eprint archive at arxiv.org. Started in August 1991 (as xxx.lanl.gov, at the Los Alamos National Laboratory), this is a fully automated electronic archive and distribution server for research papers. It is presently owned, operated, and primarily funded by Cornell University, partly funded by US National Science Foundation. Areas covered include physics and large parts of mathematics, computer science, and even quantitative biology. These main areas are split into sections; so in particular math.PR is the name of the probability archive. For historical reasons there are some differences between how the different areas are organised. Statistics is presently conspicuous by its absence.
The word "archive" does the service an injustice. In various fields, arxiv.org functions rather as a market place or forum where the latest ideas are exchanged and discussed. Anyone can submit research papers to the archive. Typically, LaTeX source is submitted, typically, PDF is retrieved. Users can register to receive automatically a listing of newly submitted papers of interest to them. There are plenty of ways to search arXiv, and more are coming. When papers are revised, the revision can (and should) also be uploaded (the earlier versions remain available); when a paper appears in a journal, a full bibliographic reference to the final version can (and should) be added.
Decent journals allow authors to self-archive their published papers. The better journals encourage authors to archive published papers on arXiv. The best actively place all published papers on arXiv too. It seems likely that IMS journals will soon be in this last category, and hopefully Bernoulli Society journals, too.
Cooperation is planned between arXiv, Google and the IMS (and hopefully the Bernoulli Society, too) to provide further search facilities within the PR section of arXiv. And last, but not least: plans are underway to split off a statistics section, math.ST from math.PR.
This route towards getting statisticians into arXiv seems a good way to start. If it takes off, who knows where it will go from there. Possibly many statisticians may feel that statistics should be a whole field alongside physics, computer science and mathematics. On the other hand, people working equally in probability and statistics will find it unnatural to have to make a choice, and the choice they make will of course have impact on how easily other people can find their work. There do exist cross posting facilities.
On a personal note, I have been working for the last few years in quantum information and quantum statistics. My aquaintance with arXiv is so far mainly limited to the quant-ph section (within physics) and my experience there, is that arXiv has been instrumental in making quantum information into a vibrant community. Everyone posts all their work there, everyone consults it regularly, and published papers reference numerous recent postings. The system adds a new dimension to the already available conferences / journals / personal / … web pages. It makes none of these obsolete; on the contrary, the whole is more than the sum of its parts. My only grudge is that the status of "cross-listed" (e.g., from quant-ph to math.PR) is not symmetric, which means that a paper will be less visible on the secondary side. This is a pity if you really want to sit on the fence!
Personal websites come and go, and their content is ever changing, but arXiv has (so far) a semi-permanent status which makes it wonderful not just as a forum and a historical archive of published works, but also as a repository for the kinds of writings which do not belong in a regular journal (such as because of length or tutorial nature, but which still, everyone needs to read and to cite).
As I wrote above, plans are underway to split math.PR into math.PR and math.ST. In the meantime, statisticians are of course free to post papers on math.PR. (Each section has a moderator; in my experience this is completely unobtrusive and the moderators' main task is to act when the system is being blatantly abused). Anyone who is not yet a user of arXiv might like to find out more about it. Register as a user and post your latest / next preprint on math.PR (even if you consider yourself a statistician).
The procedure is very easy. To get started, at the very top level, point your browser at arxiv.org and notice the "help" button at the top right of the page. You might also go directly to arxiv.org/find/math, type a likely name in the field "Author" (e.g., "Pitman") and then click on "Search". The default options will give you this person's postings of the last year. You can choose "all years" if you prefer, among many other possibilities. (You won't find me here yet: if you are interested go to arxiv.org/find/quant-ph).
An alternative and perhaps better starting point is the front end for mathematics at the URL front.math.ucdavis.edu/ but I am not so familiar with it yet.
— Richard Gill