Links for Airlines:
The earlier you book (a flight), the cheaper flight seat you find. It is recommended not to wait to book a last moment flight.
1) Ryanair: From London Stansted, Liverpool, East Midlands, Bournemouth, Athens, Frankfurt-Hahn, Brussels (Charleroi), Milan Bergamo, Bologna, Pisa, Rome Ciampino, Kaunas, Oslo Rygge and Stockholm Skavsta to Rhodes airport.  
Ryanair link

2) Jet2.com: From Manchester, Glasgow, Newcastle, East Midlands and Leeds Bradford to Rhodes airport.
Jet2 link

3) Easyjet: From Liverpool, London Gatwick, Paris Orly, Berlin Schoenefeld and Milan Malpensa to Rhodes airport.
Easyjet link

Thomson Flights: From Birmingham, Bournemouth, Bristol, Cardiff, Doncaster Sheffield, East Midlands, Glasgow, Leeds Bradford, London Gatwick, London Luton, London Stansted, Manchester and Newcastle to Rhodes airport.
Thomson link

5) Flythomascook: From Birmingham, Cardiff, East Midlands, Glasgow, London Gatwick, Manchester and Newcastle airport to Rhodes airport.
Flythomascook link
6) Monarch Airlines: From London Gatwick and Manchester to Rhodes airport.
Monarch link

7) Norwegian.no: From Copenhagen, Oslo-Gardermoen, Lulea, Stockholm-Arlanda, Aalborg, Alesund, Alta, Bardufoss, Bergen, Haugesund, Karup, Kiruna, Kristiansand, Molde, Stavanger, Tromso, Trondheim and Umea to Rhodos airport.
Norwegian link

8) Finnair: From Scandinavian countries to Rhodes airport
Finnair link

9) Transavia.com: From airports in Netherlands to Rhodes airport
Transavia link

10) Alitalia: Airline from Italy to Rhodes airport
Alitalia link

11) Tuifly.com: From Germany and Switzerland airports to Rhodos airport
Tuifly link

12) Condor: From Germany airports to Rhodos airport
Condor link

13) Airberlin: 
From Germany and Switzerland airports to Rhodos airport
Airberlin link

14) Germanwings: From Germany airports to Rhodos airport
Germanwings link


15) Flyniki: From Austria and Germany airports to Rhodos airport
Flyniki link


16) Smartwings: From Prague, Brno, Ostrava, Bratislava and Budapest to Rhodos airport
Smartwings link

17) Edelweiss Air: From Geneva airport and from Zurich airport to Rhodes airport
Edelweiss link


18) Jetairfly: From Brussels airport, Charleroi airport, Liege airport and Ostend-Bruges airport to Rhodes airport.
Jetairfly link


19) Olympicair: From various airports in Europe to Rhodes airport
Olympicair link

20) Aegeanairlines: From various airports in Europe to Rhodes airport
Aegeanairlines link