I secretly keep on wishing to build a true fanless system, but I have personally opted for something in between. A good quality PSU (fanless or with a fan only active after certain threshold), SSD drives (mechanical ones are terrible offenders about noise), a bulky CPU heatsink and good quality fans spinning at no more than 800 RPM can give you a really silent desktop for a reasonable price. If you need to add a discrete GPU to the equation you can get a not too power hungry one with decent fan regulation (they can work fanless under low workloads).
While not fanless and not a truly 0dB system, any potential noise is covered by any background noise, even in quiet places, your own keyboard typing or the audio from your gaming session if you are stressing your GPU.