I don't think I own any interchangeable lens cameras that don't have a manual exposure mode. I have no use for a camera for which I don't have this basic control.
If I'm taking my time, I prefer using manual exposure. But if I'm in a situation where I might have to react rapidly to suddenly changing conditions, often I prefer using an auto mode, and typically I prefer Aperture Priority mode. There are some situations where I prefer Shutter Priority, such as air shows and auto races, where I want to blur the propellers on prop-driven aircraft, or blur the wheels on race cars (or motorcycles).
I must state, however, that my comfort level when running a camera in an auto mode depends on which camera I'm using. There are some that I don't trust and others that I trust much more. For example, I don't trust the way Canon A-series FD cameras often react to light conditions, but with other FD Canons, such as the T70 and T90, and the New F-1, they can be set to be more tolerant of changing lighting. For the most part, I trust the metering system that Nikon employed with many of its cameras like the FE and FE2 (known as 60/40) and I trust even more the tighter method used with the F3 (80/20). Pentax and Oly metering patterns, for the most part, fall somewhere between Canon's A-series metering pattern and Nikon's 60/40 pattern. Contax and Yashica, Leica R, Minolta's MC and MD cameras -- I'm not familiar with these cameras' metering patterns. In general, just plain old centerweighted averaging can be problematic if the centerweighting isn't strong enough.
So, when in doubt, if I'm shooting outdoors and the lighting is remaining relatively constant, I'll just set the camera to a correct exposure value and just leave it there, then go about my business. In other words, I'm back to manual exposure again.