If you don't specify the camera and adapter and lenses you are talking about then the answer tends to be of the form "The sound of one dog barking".
IF the adapter is a glassless one and used only to adjust the lens to sensor plane distance then you may get little or no quality loss. Even without glass you can get effects due to different geometry.
If the adaptor contains a lens or lenses to allow for an otherwise unattainable lens to sensor distance then some quality loss will occur. A $2000 adaptor or one branded "Carl Zeiss" will have little quality loss. Practical reality says that a $100 or less will have noticeable quality loss.
As well as optical quality loss you want to check re possible partial or complete focus and aperture functionality loss. Also, lenses with inbuilt IC's need to be correctly dealt with if functionality is not to be lost.
What camera? NEX series?