I have been joking about how we should build a "total sh*t array" out of old Dish/DirecTV antennas, so that we could explore the systems design without worrying too much about whether anything could be done with the data collected. This hasn't interested my coworkers that much :) There is an amateur radio astronomy society, and there are plans for how to build various levels of radio telescope, starting from ~$50 and an old Dish receiver and going up. And our open-skies policy means that you do not have to be a professional astronomer to use our instruments, although I only know of one or two amateurs that have proposed for time. (They did get it, though).
As a rough back-of-the-hand deal, we allow anybody who gets time to access about 25 MB/s of data. The correlator we have currently (WIDAR) can certainly output much more than that, up to gigabytes per second, but the rest of the infrastructure certainly can't keep up at that rate sustained. It's not unusual for an observation to top a few TB in size. ALMA data files are probably even larger on average.
We are already in the early design stage for a next-generation VLA, which will increase the number of antennas to about 300. At that point, we probably won't be able to keep correlated but unprocessed raw data, just because of the sheer size of it.