Even though the prospects of actually
calculating a value for N are
essentially zero at this point, that
doesn't stop people from thinking about
the problem.
In fact, the Drake equation is still a neat
way to encapsulate the field of astrobiology --
not to mention summarize the course!
One approach is the just be creative
and channel science fiction energies,
for example at
this
web page.
One way to "solve" the Drake equation would be
through direct contact with another intelligent,
communicative civilization. This is the underpinning
of SETI, the Search for Extraterretrial Intelligence.