Bees are necessary for pollination along with many other insects including the tens of thousands of different types of beetle. Also some bats and birds help with pollination as well....
Most members of the grass family (including wheat, barley, rye, rice, bamboo and corn) are wind pollinated and are not dependant on bees. The grass family feeds, directly or indirectly over 90% of the World's population.
That's why the beekeepers across the States and in the UK were so worried a couple of years ago when that bug was killing whole hives of bees - no bees, no crops - no crops, no food - no people.
sidkid is right that most of the staple crops which are grasses would be unaffected as they are wind pollinated. However most other flowering plants like fruit trees, potatoes etc are insect pollinated and these would have a major problem without bees.
Currently have more hover flies pollinating at the moment, much higher numbers than bees, not many butterflies about this year,the buddleas are usually alive with them, very poor numbers, hope their numbers increase.