I haven't read through all the answers in detail, but there is one obvious possibility that I don't see anyone else having really mentioned so far: peak oil. Or more generally, peak available resources.
First a bit of background. "Peak oil" refers to the moment in time when oil production (or extraction, rather) reaches its maximum rate, or "peak". This can be on the level of a single oil well, or on the level of the entire world. I'm going to talk about peak oil here, but the same concept applies to any resource which is non-renewable within human timeframes and which the society depends on.
A very large fraction of our world's current energy mix comes from fossil fuels, and a large fraction of that is oil and gas, which are both for all intents and purposes non-renewable in time spans relevant to humans. If you (for some value of "you") are consuming a resource at a greater pace than it is renewed, it follows logically that at some point you will run out. (I'm sure there's a way to prove that using MathJax, but I don't think I need to.) Peak oil isn't about running out of oil, per se, but it does have the consequence of running out of a stable supply of cheap oil. When all that is left is deep water oil, oil from tar sands, and so on, you may very well technically still have lots of oil left, but you won't be able to get it out of the ground for cheap, and you might not be able to get it out of the ground at the rate needed. So the price goes up, causing a much greater fraction of the world's total economic output to go to energy extraction just to maintain the amount of energy required to maintain the status quo. If you normally pay 2% of your income for electricity and suddenly that figure jumps to 10%, something has to give. Now scale that up seven billion or so times. Our current oil extraction rate is on the order of 80 million barrels per day; one barrel is about 160 liters; that means we currently go through some 13 billion liters of oil every day. When the price goes up, demand eventually goes down, which is likely to cause the price to go down; rinse and repeat a few times with violent fluctuations in price both up and down as the world society at large struggles to recover. Alternative energy projects are likely to get scrapped during low price periods, and funding is likely to be scarce during high price periods.
Experts debate when peak oil will happen, but I have yet to see a credible argument that a finite resource will not eventually peak and start to decline. If a society has grown used to, or even depends upon, that resource, then the decline in the production rate of that resource is going to have an impact on the society.
The western world today is largely in such a situation with regards to oil. We use it to manufacture things, we use it to transport things, we use it to provide heat and light (by way of electricity), we use it to grow food (by way of farm machinery, which itself is constructed using oil and petroleum products), we use it to make toys and kitchenware (plastic!), we use it to mine other primary resources, we even use it to construct and maintain "renewable energy" sources such as wind power plants or solar cells.
We know for a fact that on a human time scale, oil is finite and thus if we keep consuming it at a fixed rate we will eventually run out; a plausible argument can even be made for that we are about to hit the extraction rate decline now to soon. This satisfies your first two criteria: it starts here on Earth, is a logical extension on our current situation, and there is a clear and plausible mechanism to get us from where we are to this situation.
That leaves your final criteria, that the process is unstoppable, persistent and widespread. Let's take those in turn.
Unstoppable: Once you've burned the oil, or made plastic, or whatever else you do with it, you really can't put the genie back in the bottle. Reuse of materials can go some of the way, but not all, and eventually entropy wins out. We have yet to perfect the perpetual motion machine. You can invent new technologies like cold fusion power plants, but our past results in such endeavours are not promising and it almost certainly won't get easier in an energy-constrained environment, as I alluded to above. As we require energy to even extract oil from the ground, read up on the concept of EROEI ("energy returned on energy invested"). By the time you only get a few times more energy out of the oil compared to the energy investment to get it out of the ground, extracting the oil for the energy doesn't make sense any longer. And if you do still extract it, you leave even less than you used to have for the future.
Persistent: Same as above; if by "normal" you mean our current western lifestyle, that is heavily dependent on oil (and other fossil materials) and if those aren't there, there's no going back. You can make various changes to draw out the process of change, but you can't at time $T_{n}$ go back to the state that you had at time $T_{n-1}$ in any plausible manner when going from $T_{n-1}$ to $T_{n}$ involved some irreversible process such as running an engine on some of the energy you used to have, and the energy used to go from the state at $T_{n-1}$ to the state at $T_{n}$ was greater than the total energy added to the system during that specific time period (whether that time period is on the order of microseconds or centuries).
Widespread: A fairly small number of contries are net oil producers these days and thus are capable of being net oil exporters. Everyone else must import some or all of their oil. If, say, Saudi Arabia were to hit peak oil and face a serious decline in oil extraction rates, it would have a widespread impact because of Saudi Arabia's large share of the oil export market. And sooner or later, that will happen. It already has happened to Norway, as well as a number of other countries.
By the time people are struggling to put food on the table for themselves and their loved ones, or keep warm in the winter, and that goes on for year after year, I wouldn't really expect back issues of Nature or the Astrophysics Journal to carry much value other than in terms of how much warmth you can get by burning them, nor would I expect people to spend a lot of energy on keeping Wikipedia running or accessible. At that point, while some knowledge would almost certainly be retained, a lot of knowledge that doesn't have day-to-day practical uses in such a situation would likely be lost. With how many rely on online services already, it is far from impossible that some amount of knowledge could essentially be considered lost immediately once those services shut down.
For some further discussion on this, one might consider the words written by John Michael Greer; for example, back in April 2007, in Cycles of Sustainability,
Does this mean that peak oil can be ignored, because it poses no threat to industrial society? Hardly. As oil production worldwide continues to contract, and conservation and alternative energy reach the point of diminishing returns, oil prices will spike upward in turn, rising even higher than before and unleashing another wave of economic and social disruption. Just as the economic contractions of the 1970s and 1980s spawned intractable unemployment in most industrial societies and launched a process of downward mobility from which many families never recovered, each wave of economic contraction will likely force more and more of the population into a permanent underclass for whom the abstract phrase “demand destruction” plays out in a downward spiral of impoverishment and misery.
In such a future, the periods of apparent recovery that will likely follow each round of energy shortages and demand destruction will provide little room to rebuild what has been lost. Those periods will, however, make it exceptionally difficult for any response to fossil fuel depletion to stay on course, so long as that response depends on market forces or politics. Each time oil prices slump, the market forces that support investment in a sustainable future will slump as well, while governments facing many calls for limited resources will face real challenges in maintaining a commitment to sustainability which, for the moment, no longer seems necessary. Thus the collapse of public and private funding for the alternative energy sector in the aftermath of the 1970s will likely be repeated over and over again as we stumble down the long downhill side of Hubbert’s peak.
and in the followup Where are the Lifeboat Communities? a week later,
If the industrial world faced the sort of quick linear decline imagined by so many pundits of the Seventies and the present day, the transition from a modern lifestyle to a sustainable one would be much easier. Faced with the certain loss of familiar comforts and a future getting steadily worse than the present, many people could come to terms with the difficulties of subsistence farming and learn to enjoy the acquired taste of its pleasures. As I suggested in last week’s post and elsewhere, though, this luxury isn’t one we can count on.
Instead, the most likely course for the decline and fall of industrial civilization is a cyclic process, in which periods of respite and partial recovery punctuate the downward curve that leads into the dark ages of the deindustrial future. [...]