This is a major problem in computational biology and genomics.
There are good places for the data already, NCBI, EMBL, and the like. There are reasonable places for code, Source Forge, Google Code, CRAN, with the caveat that some university tech transfer offices will see intellectual property in the code that may or may not exist. Covered, maybe even scorched, ground.
Where there seems to be a significant gap is in the availability of online resources. Availability of the code only partially addresses this issue, as many of these applications are “roll your own” endeavors that are sometimes poorly documented. Even when relatively well-documented, these websites may be difficult to replicate due to programmer/institutional dependencies.
The ideal solution for this would be a central repository run by a government agency for running web applications ala the Google App Engine, Heroku (Ruby on Rails), Bluehost (Python), or the like. This would not be a trivial endeavor, and would require sacrifices by developers, and at least some dedicated staff (in addition to the hardware). At the time of publication, the data should be placed in a publicly accessible database, and the Web application could be deposited in the government run server farm.
While I agree that dealing with these issues at the institutional level is superior to the laboratory level, only governments have the resources and permanence to ensure consistent and equal access.