The best reason I've come up with to encourage shareholders to run for the board is this:

PROTECT YOUR INVESTMENT!

For most people, and certainly for me, one's home is the biggest single financial investment we make. As if New York apartment prices aren't high enough, add the cost of the interest on a mortgage and you have a truly huge amount of money tied up in your apartment.

Serving on the board means you decide how to maintain it (replacing old pipes, repairing aesthetic damage like, saving money for future expenses) and how to improve it (buy things with a short warranty or pay for a longer warranty? establish uniform and fair methods to enforce house rules). You decide where the money goes, and how much to take in.

Other reasons:
-- Living in NYC we're lucky in that our apartments appreciate in value nearly without exception. Want to make it worth even more? Improve the building (facade, boiler, elevator), improve the financials, and give people a reason to want to live there.

-- Buying into a cooperative means you really ought to cooperate, and help each other out, even if it means serving a year on the board.

-- Those who serve even one year on the board end up knowing much more about how the building & business run, and what the co-op's possibilities and limitations are. In my own experience, nearly everyone who "retired" from the board in our building no longer complains about the building -- because they know what it's like to be on the other side, trying to resolve those complaints.

Not everyone will want to serve on the board even in the best of buildings; don't badger these folks. Focus on the ones who are fair, polite, and open to alternative points of view.

If you have a dishonest board, you may need to run a slate against them. But don't feel that's the only way. Get a couple of good people to run, and encourage them to campaign.

Let me comment on your other ideas ...
-- Term limits. Fine, but remember that you'll have to find people to fill the forced openings, and that one day you'll force out really good people. (One way around this is to limit terms of offices -- pres, treas, sec -- but not to the board itself.)
-- Requiring service. It's probably not legal, and even if it were, that would mean forcing people into something they won't contribute to. And it means that nutty neighbor with 17 cats or the all-night partier will end up deciding what's best for you.
-- Paying a nominal honorarium/maint fee abatement. Paying is dicey only because it gives people the wrong motivation. That said, waiving one month's maint fee (at the conclusion of a full year's service) would help some of us feel better about the hours of time we volunteer in the service of our neighbors.