Many good points have been made by multiple posters to this thread. I’m late to this discussion but, if I may, I have some thoughts.
My perspective is shaped by being someone unable to do my own mechanical maintenance and therefore having to pay to have all work done. The exceptions are that I keep my car immaculately clean, regularly check the oil dipstick and eyeball fluid levels, keep the washer fluid topped up, check tire pressure and keep tires aired up as needed, and on my current car (2014 Camry) am easily able to change both the cabin and engine air filters. Everything else I pay the shop to do.
As stated by others, in modern cars 100,000 miles is usually only half at worst of the distance a well maintained vehicle can easily last. Depending on climate, rust often defines useful life of a car. So, in my opinion and experience, deciding whether or not to keep a car beyond 100k miles gets down to several deciding factors: safety, reliability, comparative costs, actual need versus desire, and typical use of the car by the owner and his or her particular decison factors.
Properly maintained vehicles normally should still be safe far beyond 100k. So keep happily motoring on. In the minority of cases where a car is no longer safe and cannot be repaired to be safe within other decision factors, then replace it.
The same is true regarding reliability as safety. That said, acceptable and preferred levels of reliability vary depending on individual circumstances. Don’t confuse acceptable versus preferred. Depending on other decision factors, acceptable reliability is often a good choice to stick with even if it isn’t the preferred level.
Before looking at comparative costs, let’s jump ahead to to typical use and actual transportation needs. Those relying on only one car for transportation to work have to weight reliability more heavily than those with access to other reliably available transportation – a second car, family or friends, car pool, public transportation, etc. Also, how far is the commute, how long a wait for assistance if stranded, relative safety of being stranded in what kind of area, availability in time and distance of one or more reliable mechanic shops, availability of loaner or rental cars whenever one’s car needs to be in the shop, etc. So part of weighting the decision factors of actual transportation needs and typical use are directly tied to safety in terms of locality and to reliability in terms of both the car and available good shop and alternative transportation. And it ties into comparative costs.
Comparative costs include more than only costs of ongoing maintenance versus replacement price. Yes, as miles and age accumulate on a car maintenance costs rise somewhat. Any particular system, any given part on a car has specified proactive maintenance intervals as well as typical lifespan before needing replacement of those parts. Don’t confuse this with repairs that arise from damage situations such as hitting a curb or big pothole or other damaging events.
Ongoing costs of keeping a car include maintenance costs of short interval such as oil changes and tire rotation; intermediate interval costs such as brakes, cooling system, a/c, etc.; and long interval such as timing belt, brake lines, suspension, etc. Keep in mind that the difference in intermediate versus long interval maintenance items can vary depending on the make and age of a car and also on driving and climate conditions and habits.
Further ongoing costs include insurance and taxes. Time and miles an owner keeps a car factors depreciation into comparative cost when looking at replacement cost.
Simply put, replacement cost is how much total money is required to pay out for a different vehicle. So factor in negotiated purchase price, deduct any trade-in or sale price if any on the vehicle being replaced, all financing costs both up front and long term if any, sales tax and licensing fees, increase in insurance premiums, increase in personal property tax, etc.
Let me give several personal examples of my parents and my decisions when to retire and/or replace cars. Note, both they and I typically keep cars far more years than average.
First example, in the final years of my dad’s life he was driving far less than before although still driving for both business and personal use. He also had access to my car if needed such we could share a car for several days or more if needed. His car was almost 25 years old and had some 250k+ miles on it and was pretty well worn out. It seriously leaked and burned oil and seriously leaked transmission fluid. The engine was about worn out. The interior seat fabric and carpet were worn through in spots. The trunk leaked. The speedometer and cruise control didn’t work. One window motor was burned out. But it had very little rust on the frame, brake lines, or body. The transmission still worked fine as long as the fluid level was maintained. Dad knew he had only another year or two left he was physically and mentally capable of minimal driving. So he chose to not spend money on repairs or buying a new car. When it developed a cracked ball joint (or perhaps it was a cracked steering knuckle, I forget which) I prevailed on him to park the car and use mine as needed on occasion.
Second example, I had a twelve year old 1973 Corolla that I managed to burn out three of its four cylinders one day commuting on the highway. Despite a lot of body rust the car was otherwise still mechanically sound and servicable at 140k miles. I’d been saving money to buy a new car. So, replace at that point or pay to rebore the cylinders? I did the math. The cost of interest on and fees for a loan for what I’d need to borrow exceeded the cost of repairing the engine on the aging Corolla. But I would be able to put aside enough more into savings in two more years to afford a new car free and clear with no loan. I also had access to my dad providing transportation while the car was in the shop. So, even though I would have liked a new car I chose to repair and keep driving the old car two years more until 160k miles and then replaced it due to too much rust of both body and frame.
Third example, I had a seven year old Impala with only 54k miles on it. But from day one as a brand new car it chronically had ongoing, repeated, worsening electrical issues. It also had repeated problems with and/or failures of fuel pump (despite always filling up when down to half a tank of gas), intermediate steering shaft, steering pump and rack, transmission, engine, cooling system, and suspension despite proactive maintenance. I just happened to have gotten a “hanger queen” lemon. At seven years and 54k miles it was out of warranty, even the “goodwill” extension on a few things. Mechanics at both the dealership and independent shops advised I trade it in while it still had reasonable value and get something more reliable. They knew I no longer had living family in the area to help me and that I was no longer young. Both shops gave quotes broken down into truly needed repairs, looming repairs which were mostly for second and third time failures on such things as fuel pump and steering shaft, and standard maintenance items coming due within a year based on time and mileage. While considering those costs and doing preliminary shopping for a new car to compare total outlay costs of both choices the engine suddenly started using a lot of oil. It wasn’t leaking so it was now burning oil and a significant amount especially given low mileage and going from not burning any at all to as much as typically wouldn’t show up until triple or more miles than it had. I ran the math. Even assuming not paying to find and repair the cause of oil consumption or any additional unknown problems or failures not already looming, the anticipated costs of other needed repairs and maintenance were high enough and the time the car was in the shop chronically frequent and lengthy enough that I chose to trade in the car for a new car. Before the new car was out of warranty the difference in projected costs to keep the hanger queen versus total costs after trade-in for new purchase “paid for itself” in money saved while providing a far, far more reliable car.
So, my response has been a Very Long Discourse that can be summed up as it most usually is quite reasonable and more affordable to keep a car long past 100k miles but it depends on the decision details that vary from any given particular car and owner to another.
I now return you to our other regularly posting members who manage to be far more concise than I when commenting. 
