Most of the sounds that come from a car, excluding tire roar, are from the engine, and depending on the automaker, that engine could sound like crap, or it could sound harmonious in a way. Each engine size (# of cylinders) has its own sound characteristics, and these sounds often vary by brand and engine construction. So a Subaru 4 cylinder might sound slightly different than a Ford 4 cylinder, mainly because of engine construction, displacement, and exhaust construction. One of the critical components to the sound of the car is its exhaust manifold. This sits on top of the exhaust valves of the cylinders. For example, a Subaru WRX STI has unequal exhaust manifold pipes, or what is called unequal headers, which create that iconic Subaru burble sound from the exhaust. Also, a Mercedes AMG V8 sounds much different from a BMW V8 or a Ferrari V8.
The exhaust system is comprised of the exhaust manifold, the catalytic converter, and depending on the vehicle's setup, a series of resonators and mufflers, which are added to reduce and clarify the sound of the engine as to not make the car sound too loud or obnoxious. After the exhaust comes from the manifold, it can be divided into multiple pipes to create two, four, or even three exits at the rear. A popular modification, which is not the most challenging thing to do, is to replace the exhaust system from the catalytic converter back (a cat-back exhaust system) to get some better noises and even gain a few horses.
Sadly, today, manufacturers make vehicles with less noisy engines fitted with turbochargers, which muffle the sound of the exhaust even more. To combat this, automakers pump sound in, either artificially through the speakers or naturally from noises directly derived from the engine. This is just one of the ways automakers attempt to make their cars look and feel sportier (fake vents, fake exhaust tips, useless spoilers, fake diffusers, etc.). Although some automakers do this when it is needed, electric vehicles need to have some sort of noise so that pedestrians and passengers have something to hear. Electric cars are mandated in most countries to have some kind of noise at lower speeds, and often automakers pump in sound to the passengers so that they have some sort of confirmation that the vehicle is working. These sounds are also useful for people who are transitioning from gas to electric cars as well.
I can't imagine a future without car noises, but it is inevitable to some degree. Although gas cars will be around for much much longer (probably forever), the majority of vehicles on the road will likely be electric as the technology with charging and other issues improve.