Are trees the only source of large amounts of oxygen?
71% of the earth's surface is taken up by water. Not surprisingly therefore, the seas are an important source of oxygen. National Geographic claims that photosynthesis by phytoplankton (mostly single-celled phototrophs, such as cyanobacteria, green algae and diatoms) account for half of the earth's oxygen production. The other half, they claim, is produced on land by trees, shrubs, grasses, and other plants.  

The Ecology Global Network takes it a step further and claims that all marine plants (including phytoplankton) together produce 70 to 80 percent of the oxygen in the atmosphere. 

Based on these reports, hence, marine phototrophs account for 50 - 80% of the earth's oxygen production. 

With regard to terrestrial oxygen production, NASA reports that 30% of the land is covered by trees, and as much as 45 percent of the carbon stored on land is tied up in forests. So on land, trees are definitely large contributors to oxygen production.