Aside from billions of desperate humans futilely trying to Google why the Internet has gone out, and porn magazines seeing a 10000000000000% spike in sales, quite a lot would happen if the internet went down, even in a matter of days.
Interwebz powerhouse Reddit, always a fertile hotbed for passionate and (generally) informed discussion, had quite the chat on the subject recently—here are some of the juiciest kernels of crowd-sourced knowledge, sifted out of the sludge by yours truly.
TL;DR: No internet = bad times for everyone.
No more food
Reddit user BinarySoup explains (in the top comment on the thread) that the internet going dead for a couple days would leave ripple effects that would hamper future food supplies as soon as the next week: "Everything is done over the internet, if its down there is no way to monitor all the supplies etc that are constantly on the move. If the internet was down for a week it would be pretty devastating."
Businesses would suffer, but hospitals might be okay (for a little while)
User table_rock claims to work for a manufacturing company, saying that his business would be completely shut down during a two day blackout: "We couldn't purchase supplies, manage inventory, receive orders, fulfill the orders we already have, process payments or invoices, or even ship anything." With several other users (who have unique, professional situations) echoing this sentiment, and agreeing the shockwaves would certainly effect their overall operations for months, even years.
As far as the ever-important hospital situation, Jabberminor, a hospital employee, says "...while the hospital has its own database, it still has to extract a lot of information from outside the hospital. Either its to do with patient information, or simply just from people going on the Internet to look up stuff." So the hospital could function, just not at full capacity, because most have temporary contingency plans in place already.
Delivery would be an issue
Flaghammer gives his professional take on supply and demand, as a truck driver: "I would sit still without internet, my truck can't even get fueled without it. I don't even use a fuel card I type magic numbers into the pump that directly accesses their fuel money." He alludes to the fact that there are workarounds, but without internet access, chains wouldn't be able to restock distribution centers.
The stock market would be screwed
Knotninja writes "The stock market would likely be closed in a total internet outage. Credit transactions for purchases would stop. No bank to bank transactions....I would say a major internet outage constitutes a national emergency. Could we survive and recover? Sure, eventually. We would take a major economic hit in the meantime."
In an extremely detailed post, user ValidatingUsername states "For the average person, the fallout of the stock exchange would take a few days to weeks to be felt, however the myriad of other institutions and sectors affected would induce global panic and riots almost immediately."
In essence, no internet would spell certain doom
In one of the longest posts on the thread, heavily motivated Redditor AthleticNerd_ waxes poetic on the loss of web, in horrifying detail: "Instantly, about 80% of all services are interrupted. Television goes offline. The basis for all your information is immediately gone; cell phones, computers, TV—all of it is offline. Even your landline phones are affected. Only radio and broadcast TV still work. But, nobody knows what’s going on (due to lack of communication), so there’s little information to share."
"Traffic is snarled because lights run on computers and the computers can’t get updates. After 3-4 hours, even the public transit is taken offline...Day-to-day services also start to break down pretty quickly. Of course all the credit card machines are down, along with all the ATMs. So everyone only has as much spending money as they have in their wallets."
What about after the fallout?
AthleticNerd_ continues with "On the radio, the president finally addresses the nation, with reports of widespread looting and rioting, the difficulty for the police to keep civil order, and hospitals getting a mass influx of injuries from all the altercations and accidents; the president doesn’t go so far as to declare martial law, but he does call up the national guard to help 'maintain order.'"
And if it ever does come back: "The world has changed. When the stock markets went back up 2 weeks after the ‘net-out’, it instantly crashed and there was a renewed public panic amid an instant global depression. All caused by massive infrastructure and production interruptions. It’s finally getting to the point where basic products like milk, eggs, and gasoline are back to pre net-out levels of availability, although prices are still at record highs. Governments and militaries all over the world have been on high alert. All from a mere 48-hour internet blackout."
It's actually happened before
User Splorinstuff has some tangible experience in something like this, albeit on a much smaller scale: I live in Arizona and a recent incident made it very clear how reliant we are on the Internet. "Someone cut a trunk line in Phoenix. It knocked out cell phones and Internet through nearly the entire state. Because there was no communication (except radio) most people didn't know why everything went out."
"While in total it was probably less than 12 hours, panic was pretty clear. Banks shut their doors and dropped their bars for protection. Grocery stores told people not to come in unless they showed cash at the door. People were running all over trying to get money and supplies....Financial loss starts to seem relatively insignificant to the other effects."
So the question is: could a large-scale outage really happen?
Among the extremely technical, extraordinarily tedious arguments (ranging from terrorist attacks to wide-ranging accidents) as to whether or not the "Internet" as we know it could ever be made fully defunct, one actual, legitimate possibility arose that most people agreed upon: solar flares.
"It's quite possible if there were a solar flare strong enough to knock out the power, that we would lose the internet for days, or even months. We know that such storms are not unprecedented, so there is a good probability it will happen again at some point," noted user Kvestchunz.
"A sufficiently large solar flare could in theory blast the earth with so many EMP waves that all our electronics that make up the internet would fry. The chances of this are extremely slim but it is possible," Spear99 added.
On a positive note, at least everything wouldn't be horrifying
Several users noted the likelihood of waves upon waves of "blackout babies"; with internet loss would come massive bouts of boredom, and free-wheelin' sexytime would likely be a'flowin in no time. Not to mention "THIS IS THE END OF THE WORLD, WHO CARES?!" is basically the best pickup line ever.