Hybrid Personal Rapid Transit
When I was in high school, I did a project on PRT -- Personal Rapid Transit. It was the "next big thing" in transit and of course, 30 years later it's still not here, in spite of efforts by various companies like Taxi 2000 to bring it about.
With PRT, you have small, lightweight cars that run on a network of tracks or monorail, typically elevated. "Stations" are all spurs off the line, so all trips are non-stop. You go to a station, often right in your building, and a private mini-car is waiting. You give it your destination and it zooms into the computer regulated network to take you there non-stop.
The wins from this are tremendous. Because the cars are small and light, the track is vastly cheaper to build, and can often be placed with just thin poles holding it above the street. It can go through buildings, or of course go underground or at-grade. (In theory it seems to me smart at-grade (ground-level) crossings would be possible though most people don't plan for this at present.)
The other big win is the speed. Almost no waiting for a car except at peak times, and the nonstop trips would be much faster than other transit or private cars on the congested, traffic-signal regulated roads.
Update: I have since concluded that self-driving vehicles are getting closer, and because they require no new track infrastructure and instead use regular roads, they will happen instead of PRT.
Yet there's no serious push for such systems...
Read on. Most PRT designs require special custom cars with the ability to accelerate and brake very quickly, so the station spurs can be short. You can play some tricks by creating gaps in traffic to allow breaking/acceleration on the main line, but only to a limited extent and with safety risk.
One of PRT's flaws is that it's more like a taxi. People like to personalize their cars and keep their stuff in them. And of course if you are not near the station, you still have to get to and from it, in the weather, etc.
I suggest a Hybrid PRT vehicle, which is also a small electric "city car" like the TM Th!nk or the Smart in size and design. (Actually its size and design are more constrained by the parameters of the PRT track.) This car would have batteries only for modest range (say 10km.)
People would buy these cars, and keep them at home or office with a charger. They would have range for local short city errands, and of course to get to the PRT track and a grade-level entry/exit station. There they could drive into the special station and let the PRT system take control of their car. The car might be driven by providing an electrical connection to run the car's electric motors, and there could also be magnetic induction for the quick starts/stops in stations as needed.
Once the system delivered the car to a station, the car could drive out if it had further to go, or more commonly the passenger would just alight at the station. At that point, some owners would elect to rent their car out to the system. Such cars would have two trunks, one always for the owner's permanent gear and one for any user. If enough people did this, the system may not need to own many cars of its own.
If the owner is a commuter with decent plans for when they want the car next, the car would of course be scheduled to be ready at the owner's stop at that time, or nearby and summonable on short notice. If the owner wants it at an unexpected time, options could include providing a free rental replacement, or requiring the current occupants to change cars at the nearest station, and then whisking the car to the owner. It could be arranged that the car never goes more than a few minutes travel from where the owner is. (Those who want longer trips are just never assigned such a car.)
Other owners would elect not to rent out their car. Their cars would be whisked, empty, to a storage yard (parking lot equivalent) not too far away. A cell phone signal just a few minutes in advance would have the car waiting at the station.
Ideally the standard car size would be built on an existing popular chassis for a regular car, to make production cheap. It's also possible to imagine the hybrid having a gasoline engine. If it's electric, the weight of the battery may be a question. One solution is to have a small battery, with range only for short trips.
Another idea is to have a fancy modular battery system, with automatic machine swap-out possible. The car would be moved to the battery swap station where robot arms could quickly remove the battery at the start of a trip (storing and recharging it). They could also attach (on egress, probably) different sizes of batteries, so those needing to travel far from the PRT system could do so. Like the cars, batteries could be rented out to others. You probably don't need to get your exact battery, but since batteries have life-cycles, this would need to be tracked so it all remains fair.
However, due to the delays involved and the extra logistics, it would ne nice to get the system going without the battery swap, then add it for efficiency and flexibility. If the battery remains in the car on the network, ideally it would be recharged while moving. This does mean a somewhat dangerous high-voltage power system, but modern electronics can make that safe. Also, if cars have batteries, temporary safety interruptions of the power are not a problem. (Totally in-system cars would need a small battery able to get them past power gaps.)
The result would be a transit system people would actually use. Fast, no-driving, non-stop transport (so you can read or work on the trip) with no stops would beat out cars every time for a radius of several km from the track system. The track itself cheaper and smaller than roads or rails. The cars paid for mostly by the public.
There are a few things it can't do, such as readily emptying a stadium. To do this, people may need to walk a bit to get to multiple stations, or traditional multi-passenger busses could take people 60 at a time to a network of stations which can distribute the load. Special stations designed for bulk departure and arrival could also be built.
Rush hour is a problem for all transportation systems of course. PRT might be cheap enough that the system could be built closer to being able to handle the peak load. Instead, at rush hour, people might arrange PRT "appointments" where the track-segments needed for their trip are reserved. If the system is overloaded, they can at least relax and work before going to the station at their appointed time.
It's also worth considering that PRT has a long history of failure, and there are some good arguments about why it's one of those things where theory and practice differ a great deal. On the positive side, technology is rapidly improving (especially computers, and some materials) and we often forget just how much of our land we devote to the real alternative, the automobile. When you consider the true cost of the car, even way over budget PRT (and LRT) sound pretty good.