Pertaining to the arts (painting, music, literature, etc.), the word classical often refers to a specific time period or artistic style:
Classical architecture originated from Roman and Greek construction methods, which were later used as a model for "neo?" and "revival" architectural styles
The word 'classical' is applied to any mode of scientific thought prevalent up to the time of some radical new innovation, or any scientific area of study that has well established roots, typically pre-nineteenth century.
Classical mechanics, in physics, as founded by e.g. Galileo, Newton and formalized by Hamilton and Lagrange (developed before the advent of modern quantum mechanics) (see also the page about classical physics)
Classical mechanics is Newtonian physics, i.e. physics as it was before special relativity and quantum mechanics. In other words, the limit of physics as c2 goes to infinity and h goes to zero.
Semiclassical physics, an approximate solution to a problem generated by assuming that for parts of the system, the results of classical physics does not differ too much from that of the quantum mechanics method.
Classical logic, in mathematical logic includes the family of bivalent logics where every proposition is either true or false.
"Classical control theory" applies control theory to analog systems. Based on classical math methods such as Laplace transforms and calculus, as opposed to the more recent digital control systems theory - based on more modern methods such as the z transforms.