Just to embellish stelz's comment that the use of 2/2 vs 4/4 notation is a matter of how many "pulses" there are in a bar (2 vs 4). While, seen from a distance, each bar of 4/4 ("common time") and 2/2 ("cut time") music might look similar (4 quarter notes to a bar), this is not only a mathematical quirk of music notation. It has implications as to tempo for music of the Baroque and later, which is why composers chose one time signature over the other. I can think of no better example comparing the two notations than the first and last movements of Mozart's Haffner Symphony. The former is in cut time (2/2) while the latter is in 4/4. The last movement is also marked Presto. 4 pulses the bar at a Presto tempo should result in a frenetic pace to the movement -- and Mozart is on record as wanting his really fast music to go as fast as possible. The first movement, on the other hand, is marked Allegro con spirito and its two pulses to the bar will end up with the quarter notes slower than in the last movement. This notation is (or should be) very helpful to performers and, especially, conductors, who need to establish the tempo for a piece, like the first movement, that can conceivably be played at any number of speeds, unlike the as-fast-as-possible last movement. Try conducting along (or even just tapping your foot) to the basic pulse values, and then, for comparison, along with each quarter note in each movement and you'll instantly feel the differences.
--Sixtushttp://erato.uvt.nl/files/imglnks/usimg ... __K385.pdf
Other examples of really fast 4/4 Mozart: The Marriage of Figaro Overture, the faster and faster Finale of the 2nd Act, Finale of the 4th Act. Don Giovanni, finale of Act 1.
Example of not quite as fast 2/2: Don Giovanni Overture
Example of extremely fast 2/2: Don Giovanni Act 2 Final scene (marked Presto, i.e. 2 presto pulses to a bar, which results in extremely fast quarter notes)