CVT are getting more and more popular due to higher fuel efficiencies and better performance from smaller engines. Some manufacturer's like Nissan, have actually pushed CVT to almost all of their offerings. CVT technology has been around for a long time, so it had been pretty well vetted - shown to be very reliable.
That said, doesn't mean that they are well liked. Because they favor efficiency above all else, they have a certain behavior that some people just can't get used to. Some CVT manufacturers have tried to address this by having "virtual" gears, so that the tachometer rises and falls like it does on a conventional automatic. Some have addressed the droning / motorboat noise from the engine and transaxle running at peak RPMs. Performance-wise it is great, from an audible standpoint, sounds like someone farting down a tube. Again, manufacturers have addressed this with pumping an inverse waveform through the speakers to help cancel the sounds or some cases, make the car sound different inside the cabin.
Myself, I'm torn between them. From the engineer / scientist perspective - I see great utility in a CVT design. But from an owner / operator standpoint - see more value with audible and physical aspect of separate gears.