We start from the end: sweets are most famous Sicilian food. The first are Sicilian cannoli, made using fresh sheep's-milk ricotta filled in a tube-shaped shell of fried pastry dough. We remember also icecreams and the granita.

What's that? Granita is Italian ice, but you can find the best in Sicily. If you came to visits Sicilian cities remember to sitting in the café in the morning and having a Granita di Limone and brioche for breakfast. Yes, in the summer in Sicily, granita and gelato are breakfast foods. You can experience lemon taste, or coffee or (probably the best) almond.
Finally, don't forget the “cassata”, a Sicilian dessert which owes its existence to the medieval Arabs of Sicily.
How this occurred is a question of agriculture. The Arabs introduced sugar cane, and this revolutionised Sicilian cooking. Before the ninth century local honey was used to sweeten Sicilian pastries.
Cassata is a tort of plain white cake filled with the same sheep's milk ricotta (cottage cheese), topped with frosting and sugared fruits. It is traditionally a winter and spring dessert served around Easter; in Sicily sheep produce little milk in summer, and frostings would melt under the torrid heat. Its name is believed to derive from the medieval Arabic kas'at in reference either to its circular form (more precisely the pan used to mold it) or the word for cheese products (cascio akin to casein).

Jewels from Sea
The best Sicilian seafood dish made with pasta is finnochio con sarde (fennel with sardines). But don't miss (for no reason!) rolled stuffed slices of swordfish, you can find the best in eastern Sicily.
Strange balls of rice

Like the cuisine of the rest of southern Italy, pasta plays an important part in Sicilian cuisine, as does rice: for example with arancini, glorified deep-fried stuffed rice croquettes, celebrated in a recent best-selling Italian novel (“Montalbano's Arancini”, by Andrea Camilleri). The original recipe takes 2days to cook…
Also important are cheeses, Sicily has spawned some of its own, using both cows and sheeps milk, such as pecorino and caciocavallo. Spices used include saffron, nutmeg, clove, pepper, and cinnamon which were introduced by the Arabs.
Other delights
If you are a vegetarian, don't miss caponata, a tasty salad made with eggplant (aubergines), olives, capers and celery, makes a great appetizer. There is also an artichoke-based version of this traditional dish, though you're less likely to find it in most restaurants.
Sfincione is a local form of pizza made with tomatoes, onions and (sometimes) anchovies, you can find it in Palermo. Prepared on a thick bread and more likely found in a bakery than in a pizzeria, sfincione is good as a snack or appetizer.
Panella is a thin paste made of crushed or powdered ceci (garbanzo) beans and served fried. It's a Palermo specialty. Maccu is a creamy soup made from the same bean.