Quite a few readers say Echelon is perfectly doable (scroll down to get caught up). Some say doable, but not worth the effort. A Phd student in physics at a fancy-pants school offers this primer:

Hi Jonah,
Another reader claims that Echelon would be technically infeasible,
due to computational and infrastructure requirements. This is not
true, as can be shown with a quick calculation. Assuming 1 billion
email users, each receiving 100 emails a day, of average length 1
kilobyte, we have 100 terabytes of data a day, or just over a
gigabyte a second. That’s more than your home computer could handle,
but really not all that much–it would probably only take the
equivalent of a thousand or so home computers. Modern supercomputers
are many times more powerful than that.
How could the email actually be intercepted? Intercepting every
single email would be difficult, but the bulk of all email traffic
could be monitored by tapping a small number of high-capacity
communication links (the “internet backbone”).
Emails would probably be processed in multiple rounds, with only a
small number being tagged in the first round for further inspection.
First-round inspection would probably consist of checking the sender
and receiver against a watch list, and scanning the contents for
certain keywords. This process would be easy to accomplish in an
efficient manner. Emails tagged in the first round would be subjected
to a more detailed computer analysis, followed ultimately by human
analysis if required.
While Echelon may be feasible, I’m not sure it’s actually worthwhile.
Powerful encryption software has been freely available for a long
time, and any intelligent criminal or terrorist would make use of
this software for their illicit communications. In particular, Al-
Qaida is known to make use of such software. Furthermore, through the
use of steganographic techniques, even the existence of an encrypted
message can be hidden by concealing it inside seemingly-innocent
images or text.
Until we have the means to decipher these forms of cryptography (and
I’m working on that), Echelon-like systems are a waste of money which
would be better spent on conventional fieldwork-based intelligence.