Currently less than 1% of the ocean is protected.
Greenpeace has been campaigning to set aside a large amount of the ocean as a "marine reserve." http://www.greenpeace.org/international/en/campaigns/oceans/...
Crops are grown on private property and the ocean is a shared resource. See tragedy of the commons.
The other problem is that just because something is a shared resource does not mean that it is automatically a lost cause. See tragedy of the commons:
Elinor Ostrom found the tragedy of the commons not as prevalent
or as difficult to solve. She and her coworkers looked at
how real-world communities manage communal resources, such as
fisheries ... and they identified a number of factors conducive
to successful resource management.
If the shared portion of the ocean were to be destroyed (over-fished or polluted) then I dare say that the unshared portion would be, too.
Studies have consistently shown that organisms within marine
reserves tend to grow larger and live longer than individuals
in adjacent unprotected areas. Monitoring results from 89
no-take marine reserves around the world have shown that, on
average, fish density, biomass, size, and diversity all
increased within marine reserves (Halpern 2003, Lester et
al. 2009). This is very important because fish that are larger
and older tend to produce significantly more eggs and larvae
than smaller fish. Also, larvae produced from older fish tend
to have a higher survival rate (Francis et al. 2007) [^1]
For reasons not fully understood, when areas are closed
to fishing, snapper aggregate within them, forming large
resident populations. Spiny rock lobsters (crayfish to New
Zealanders) do the same. Their density inside the reserve is
about 15 times higher than outside. Commercial crayfishermen
have cashed in on the reserves success because the outward
migration of crayfish—a process marine biologists call
spillover—brings the crustaceans to their pots, strategically
placed just outside the boundary. These former skeptics are
now some of the reserves staunchest defenders. They refer to
it as our reserve and act as marine minutemen, reporting
poachers and boundary cheats. ... Reserves where fishing
is banned are now seen as potential stud farms and fish
hatcheries, replenishing the surrounding seas. [^2]