I'm reading it for English class currently and it's got my curiosity stirred. How many people actually lived like that? What caused it all to stop?
As to the accuracy, it's obviously fiction, but it's strongly rooted in reality. Was there a Jurgis? No. But there were thousands of immigrants who lived the life Sinclair describes. The life of the Rudkus family could have been the life of any of the families that came to Chicago in the late 19th - early 20th C. The hardships of life and day-to-day realities of work, home, and politics are largely accurate.
If you'd like a scholarly look at The Jungle, look for a copy of Jim Barrett's Work and Community in "The Jungle"
How many people lived like that? Don't know an exact answer, but it's many thousands. Censuses were a bit haphazard at the time, and there was an itinerant nature to some of the immigrants at the time, making counts inaccurate or unreliable.
What caused it to stop? A lot of things, really. As a labor historian, I tend to put unionization at the front of the list. The United Packinghouse Workers did a pretty good job of organizing, inspite of numerous and diverse attempts by the packers to deflect union activity. See, among many others, Rick Halpern's Down on the Killing Floor for more on this.
Credit must also go to the various social reformers of the day, notably Jane Addams and the Hull-House movement. They worked tirelessly on behalf of immigrants and children. Their work brought the plight to the attention of the (generally) wealthy, civic minded folks of Chicago and they brought about many labor reforms.
It's a little ironic that Sinclair wrote the book as a socialist rallying cry against the worst abuses of capitalism, and while labor reforms certainly did happen, the major legislative outcome was the Pure Food and Drug Act of 1906 (1905? I forget.) This law set rudimentary standards for food safety and purity. Folks who read the book were apparently more upset that their meat product may contain various limbs workers lost than they were that the workers lost their limbs.
On Addams, see most any of the 6.02x10^23 books that have been written about her. I like Lucy Knight's Citizen: Jane Addams and the Struggle for Democracy. It's a big ol' book, but it's really well-done.