Trains still derail and collide just like they did a century ago. The most dangerous condition for passengers is loss of livable space--the car (and passengers) is crushed. This occurs in a collision or if the train derails at high speed into something solid. Also problematic is derailing off a mountain side or into water.
If the passengers are released from the train car, as happened in New York City's Metro-North derailment on Sunday, the passengers are potentially equivalent to being in a car accident without fastened seatbelts. Unfortunately train car windows have conflicting design goals. They must open easily if the train is on fire or the doors are crushed, but hopefully remain intact if the train goes off the rails.
Most collisions are caused by human error; the driver does the equivalent of driving through a stop light. Most derailments are caused by equipment failure. High on the list is broken rail, wheels or axles. One of the few human related causes that can derail a train is going to fast on a curve; as happened this summer in Spain killing 79. Early reports of the Metro-North driver going too fast, applying the emergency brakes or even brake failure will be quickly resolved when the National Transportation Safety Board reviews the train's black boxes. I am unaware of any passenger fatalities caused by brake failure in the modern era.
Problematic in the crowded northeast corridor is tracks laid out in the 19th century when trains traveled much slower. Urban development prevents laying out larger radius curves. In fact the radius problem is such that Amtrak's 150 mph Acela uses a train that tilts and creates its own high speed bank angle--like a banked turn on a racetrack. Tilt trains, because of increased complexity, are rarely used; and not the first choice of train designers.
There is in fact safety equipment to prevent going too fast on curves. Automatic Train Controls (ATC) has been in place on the Northeast Corridor (NEC) for many decades; and on some connected commuter lines. It is unclear if any of this technology was in place on this line. Newer technology, called Positive Train Control (PTC), was mandated by Congress after the 2008 accident in Los Angeles in which the driver, busy texting, drove past three stop signals at 43 mph head-on into a freight train traveling at 41 mph. The commuter locomotive was compressed 16 feet and shoved 52 feet into the first passenger car killing 25.
Both PTC and ATC have trouble balancing the difficulty of stopping a heavy freight train and a lighter passenger train with the same algorithm. (A freight train stopped too abruptly can derail!) Positive Train Control was supposed to be completed by the end of 2015. A recent study by the Federal Railroad Administration concluded, because of technological difficulties, the deadline will not be met. The difficulties include lack of band-with in crowded metropolitan areas and equipment incompatibility.
Trains must pass seamlessly from one company's territory to the next. When the PTC mandate was passed; in 2008, there were nine different PTC systems under development; all incompatible. Some readers may remember the incompatibility problem that existed between Apple computers and PC's for many decades. Fundamentally Apple defined their 8 bit processor as 0 1 2 3 4 5 6 7; IBM set the standard with their processor operating in reverse order. The incompatibility problem was never solved until Apple redesigned their chipsets to be PC compatible well into the 21st century.
Self-steering trains have always been, and always will be, safer than the competition. People have long since forgotten how dangerous horses were. With far fewer people and vehicles; there were about four pedestrians killed per week in NYC in 1867 by horses.
Depending on which bit of history the statistician wants to grab; train travel is nearly 20 times safer than traveling by car. Trains are in fact so safe that a single accident skews the statistics. Excluding the 2008 Los Angeles commuter train disaster trains are 45 times safer than cars. In fact, not including pedestrians (suicide by train is a problem) and car crossing accidents it is believed there has not been a fatal passenger train accident in New York City in over 50 years.