Being a fan of the "English style" Guardian cryptic crossword, I thought I'd check out the Italian ones - larsen recommended La Settimana Enigmistica, a classic which hasn't changed format since its inception. In fact at the edicola there are about a dozen magazines toting the same crossword + rebus + jokes format, though not the famous Settimanale when I looked.
The clues are more or less straight-forward, similar to "quick crossword" clues. Rather than the symmetrical grids of white and black cells favoured in UK, most puzzles are the American style grids, largely white, with most words crossed at every point, and very few blacked out cells (often placed haphazardly rather than aesthetically.)
I think that when I can do one of these crosswords I will be able to say that I really know Italian. It doesn't just required a good vocabulary, but also general knowledge - of TV presenters, the fact that Charlie Chaplin's tramp character is called "Charlot" (with a French pronunciation apparently) and so on.
The favoured layout seems to create a fair number of 2 and 3 letter words. Unfortunately, there aren't all that many 2 and 3 letter words in Italian, so rather than change the layout, the preferred solution has been to write really bad clues instead, and relax the convention that the word be a word. "Lega Italiana di Naturisti" --> "LIN", and "Schopenhauer's initials" are 2 of the better ones. "Meta' casa" (half the word "casa" --> "CA"), "Gli estremi del boom" --> ("BM")...
(Apparently the recommended publication had better clues).
There are also barred grids (like those used by Azed in the Observer), and "self-defining puzzles" like the ones popular in Finland where the clues are in the non-light cells. A nice innovation I thought, are the grids where you are told how many black cells there should be, but not where they are located.
There are also some cartoons, most of which seem to be about how hilarious it is that women shop so much. A peculiarity is that when the cartoon has no words, the editor seems to think it necessary to give the caption "Senza parole", perhaps in case we would otherwise think the words had been lost by printers error. (Which reminds me of an Italian TV guide which captioned every picture from a film "Una scena dal film").