Do you mean fell towards the sun? I’m not sure how long we would have, but I would guess a matter of days. Before that, the weather would be severely disrupted with probably very fast winds in a lot of places that would destroy a lot of regions due to storm damage. Many people would start to get rather cold (although not critically) on the dark side of the planet. On the lit side, people would suffer as the radiation would slowly destroy the ozone layer and eventually start to raise the temperature severely.
It would not be nice, and it would not end quickly either.
I think this got asked somewhere else. Firstly, gravity doesn’t rely on spinning, so we would still be able to walk around. Things would get really weird. Some of what Nazim says would probably happen, but weather patterns would be very strange due to the temperature difference between dark and lit side. Ocean currents would change.
The worst places would be directly in line with the sun. Around the edges (the terminator) it would be more like the land of the midnight sun – permanent twilight or just-darkness.
Plants would die on the dark side, they might thrive on the light side. I think a lot of holidays would be in order.
Although the spin of the earth that makes our days has been slowing down a tiny bit ever since it was formed, it’s not likely that it will ever lose enough energy to completely stop spinning, either on its axis or around the sun.. so it’s not really something to worry about!
But if it did happen, and the earth just stopped turning, then one side of the planet would get very hot and dangerous doses of radiation, and the other side would just get colder and colder. As long as we weren’t knocked out of orbit, we could stay going around the sun with one side facing, it all the time – called ‘tidally locked’ or we could slowly rotate so that all sides of the Earth got some sun each year. In that case, life on earth might be able to adapt to cope with essentially Very Long Days.