John Cage
schoenberg
There is no definitive answer for this question. Ask 1,000 people this and you will get a thousand different answers, each worthy of being correct in its own merits. What seems to be a great composer...
He has several. Fur Elise bagatelle for piano, Symphonies 5 and 9 for orchestra are a handful.
The most famous composers include Mozart, Beethoven, Bach, Mendelssohn, Strauss and Wagner among others.