What would happen if there were no more spiders?
Spiders are extremely important predators, both in "natural" ecosystems and in agriculture. They therefore function as biocontrol agents, and without them we would suffer larger crop damage from pest insects (or would require much higher levels of pesticide use). Loosing them from all natural ecosystems would also cause enormous effects, due to cascading effects through the foodwebs. The effects would differ between different ecosystems though (with the largest effects probably in forests and grasslands, see links 3 and 4 below), and nobody can really overview or predict the full implications.


  A new study reveals some stunning estimates about just how much the world’s spiders eat annually: between 400 and 800 million tons of insects, springtails, and other invertebrates. In the process, these eight-legged carnivores play an important role to keep countless insect pests, especially in forests and grassland areas, in check.   


(from third link below)

For more, see e.g.:


Rusch &amp; Bommarco. 2016. Agricultural landscape simplification reduces natural pest control: A quantitative synthesis. Agriculture, Ecosystems &amp; Environment  
Öberg &amp; Ekbom. 2006. Recolonisation and distribution of spiders and carabids in cereal fields after spring sowing. Annals of applied biology. DOI: 10.1016/j.agee.2016.01.039  
Spiders eat astronomical numbers of Insects (popular overview of paper below)  
Nyffeler, M. &amp; Birkhofer, K. (2017). An estimated 400-800 million tons of prey are annually killed by the global spider community. The Science of Nature