Tl;dr: Almost all of it. How long depends on what kind of ecosystem.
Think about your basic trophic trees from high school biology. If the plants don't produce pollen, they don't reproduce, eventually they all die. If the herbivores have no plants to eat they all die as well. Then the carnivores die, and then the land becomes a barren wasteland, with some algae-based food-webs scratching a living where they can.
The time frame for this will be relatively fast (on a geological time frame). Within a year or two all of the annual plants will be gone, their seeds having sprouted, grown and died. Tree and perennial species will begin dying off more slowly, depending on their lifespans. However, this process will begin to snowball, because the lack of plant life will contribute to climate change and without reproduction, any loss of life would be devastating.
Furthermore herbivores will begin eating every green thing in sight, after the grass begins to die off (this will take some time, since grass can grow to some extent without pollen), leading to further decline in the survivability of plants.
Some animal life could survive by eating non-pollen-based photosynthetic organisms, like algae. Additionally, plants that could reproduce vegetatively would last longer (like potatoes and strawberries). The issue with vegetative reproduction is that it doesn't increase genetic diversity, this leads to a population unable to respond to changes in the environment, and with all the plants dying there will be a lot of changes in the environment. They will last longer, but not survive indefinitely, at least not without human aid.
That being said, decomposers will have a field day for a year or two, and you can expect to see a lot more mushrooms and the like. So expect the prices of fungal foods to plummet, at least until life stabilizes to a barely-scratching-out-a-living stage.
To sum up, most food chains will collapse, but the time frame will vary greatly depending on the ecosystem of the area. Forests will have trees for many years, and grasslands will have some sustainability, depending on the durability of the grass. Somewhere like a wetland would die very quickly. Animal life would follow the death of plants relatively quickly. An ocean biome would be almost unaffected, since no oceanic photosynthesis-capable creatures use pollen to reproduce.