The word salume may remind you of salame (salami). Salame is a type of salume. Salumi (plural) is the generic word that we use to refer to salame and other cured meat products.
The web site of the Istituto Valorizzazione Salumi Italiani (IVSI) is available in both Italian and English and has a lot of useful information on the different types of salumi and how they are prepared. IVSI is "a voluntary and non-profit Consortium, that was established in 1985 to meet the growing requests made by consumers for more information while also aiming at enhancing the image of Italian processed meat products, by promoting this gastronomic heritage." It is, indeed, a rich — and delicious — heritage.
I grew up eating a variety of salumi. Every year, my father and my aunt Lucia would purchase half a pig and we received part of it raw, in the shape of braciole (chops), salsicce (sausages), etc., and part of it as salumi. Besides well-known prosciutto and salame, there are other salumi. On this page, there is a list of salumi, divided into crudi (raw) and cotti (cooked). I suggest that you avoid reading this on an empty stomach. Note that bresaola is the only one of the products listed that is made with beef (the others are made with pork).
Salumi are sold in a salumeria by a salumiere, as mentioned in a previous post. You also buy formaggi (cheeses) at a salumeria. The smell in such a store is heavenly. In the salumi department, my top three favorites are: prosciutto crudo, bresaola and salsiccia secca (dried sausage). The latter is something my aunt Lucia had. You could eat one all for yourself, thickly-sliced, accompanied with fresh bread.
The photo shows one of the panels of the lower basin of the Fontana Maggiore, the gorgeous fountain that dominates Perugia's main square. The relief portrays the month of Dicembre (December), by way of showing the slaughtering of a pig (here there is an explanation of that and all the other diptychs that form the lower basin of the fountain). Every part of the pig's body would be used, not just the meat.
A final linguistic note. Calling someone a salame is not a compliment, much as we like the actual product. Salame, referring to a person, in fact, means silly, simpleton.
Many thanks to Michael for his word suggestion and also for sending me the link to this interesting article on salumi in the East Bay Area.