It's well established that the elderly people don't usually develop
as strong or persistent an immunity from flu shots as younger people
do, but it's much better than nothing, and it's the frail elderly in
nursing homes who often end up hospitalized or dead when they get
the flu.

The Ontario government has had a policy for the past 5 years or so of
vaccinating as much of the population as possible, to protect these
very susceptible people by reducing the spread of the virus so they
are less likely to be exposed to it.  Every year, for several months,
there are free flu shot clinics in convenient places like shopping
malls, so you don't even have to go to your doctor for one.

This is one advantage of a single payer medical insurance scheme --
you can do global optimizations like this.  It's cheaper to vaccinate
the general population than to have the hospitals full of nursing
home residents with pneumonia in the flu season, aside from the
misery, disruption and loss of working time that flu causes to people
whose lives aren't endangered by it.

IIRC, most Canadian provinces have similar policies now, and the
reduction in emergency room visits, hospitalizations and deaths from
flu and pneumonia among the elderly have apparently been significant.
There's a big statistical study (another advantage is having all the
data available in one place) at ICES (Institute for Clinical Evaluative
Studies -- www.ices.on.ca) in progress right now.  I don't know when
the paper will be out.

Btw, anyone who would like to learn more about influenza, its biology,
epidemiology, etc, might like to start at www.cdc.gov/flu.  There's
also a lot of good information at the WHO site
(www.who.int/csr/disease/influenza/en), including material about the
avian flu epizootic in east Asia.