Will animals and plants that die today become fossils?

Yes, if the conditions are right. Many organisms will decay quickly, as sunlight, water, or air interacts with them. This is especially true if the organisms do not have hard parts. If the organisms do have hard parts, those that are quickly buried have the best chance of becoming fossils, as soil stops much of the decay. Most of Earth’s future fossils will be from oceans, lakes, and rivers because these are areas in which quick burial and fossilization will most likely happen because dirt and other sediments quickly pile up over dead plants and animals in such places.