The following airlines operate regular flights to Madeira:

Easyjet | There are flights coming from London, Lisbon and Bristol. Tickets start at appr 50 Euro one way.
Air Berlin | Flights from all major airports in Germany, Austria and Switzerland.
Finnair | Many flights operating from the Scandic region to Funchal.
Lufthansa | Flights from all major airports in Germany/ Austria and Switzerland.
TAP Portugal | There are flights coming from New York and Los Angeles. Tickets start at appr 400 Euro one way.