Yes, planes can often lose parts in midair, due to extreme turbulence, overstressing the airframe, other pilot error, part failure, or poor maintenance. The aircraft often can still keep flying, and even land safely (or at least make a survivable crash). Since planes may have redundant or complementary systems on either side of the aircraft (ailerons, flaps, elevators, etc.), loss of one may not NECESSARILY result in an unflyable condition, especially if the pilot recognizes the condition and compensates for the slower reaction time, adverse yaw input or other reactions of the aircraft. Loss of a rudder may have far more significant effects, however, since there is usually only one of these. Even this can be managed to some degree, especially in a twin-engine craft, but it's a LOT tougher.
Unfortunately, one of the main reasons that you see airplane parts in the mountains is that planes tend to encounter the worst weather in these regions, and flying into a vicious, unseen thunderstorm can often cause the airframe to come apart, with the updrafts and turbulence spreading the parts over many miles from the primary site. That may be why you may find only one part of an aircraft. In addition, during accident investigations, it is much easier to spot and collect aircraft parts in a prairie field, for example, than in the Rockies or the Sierra, or heavily forested areas.
All pilots know (or should know) to avoid cumulo-granite clouds (clouds with rocks in them!).