The vast majority of Madeira's visitors stay in Funchal, most of them in the Hotel Zone to the city's west. Funchal has everything from 1970s two-star hotels to five-star opulence. The most stylish and quintessentially Madeiran accommodation is hotels created out of quintas, the island's old mansion houses.
Renting a flat or a villa through popular booking websites has become popular in recent years, though it's not as widespread as in other destinations.
The archipelago has just two formal campsites, in Porto Moniz and on Porto Santo. However, Madeira was made for wild camping and bivouacing, so much so that there's a special website (www.madeiracamping.com) to help you do it. There's info on where to camp, how to apply for permission and where to buy gear, plus the site covers the entire archipelago including, rather enticingly, the Desertas Islands.