There are tons of airlines that offers flights to Gothenburg. The majority of the airlines fly to the big Gothenburg Landvetter Airport which is considered being the main airport for Gothenburg. The only airlines that fly the small airport called Gothenburg City Airport are RyanAir, Wizz Air and Gotlandsflyg.
Gotlandsflyg has a flight between Gothenburg City Airport and Visby, Gotland.
RyanAir has flights to Gothenburg from a total of 14 different locations. The 14 RyanAir destinations are: Alghero, Alicante, Barcelona-Girona, Brussels South-Charleroi, Edinburgh, Glasgow-Prestwick, Frankfurt-Hahn, Kaunas, Klagenfurt, London-Stansted, Malaga, Marseille, Milan-Orio al Serio, Pisa, Rome-Ciampino, Trapani and Weeze.
RyanAir plane on it’s way to Gothenburg, Sweden.
Wizz Air only have flights to Gothenburg from Budapest and Warsaw.
A total of 30 different airlines have flights to Gothenburgs second airport Gothenburg Landvetter Airport which is considered to be the city’s main airport. The 30 different airlines are: Air Berlin, Austrian Airlines, Air France, AirBaltic, British Airways, Sun Air of Scandinavia, B&H Airlines, Blue1, Brussels Airlines, Cham Wings Airlines, City Airline, Direktflyg, easyjet, Finnair, Iceland Express, Iran Air, Jat Airways, KLM, KLM Cityhopper, Lufthansa, Lufthansa Cityline, Augsburg Airlines, Malev Hungarian Airlines, Malmö Aviation, Scandinavian Airlines, Turkish Airlines, Viking Airlines and Widerøe.
I think it is safe to say that you won’t have any problems finding flights Gothenburg even if you are on another continent as you have big airlines with direct flights between Gothenburg and big European flight hubs.
If you are on a budget you should have a look at RyanAir which sometimes offers flights to Gothenburg from as little as 1 EUR. Lufthansa and Scandinavian Airlines have also lowered their prices significantly to compete for the passengers. The two later airlines offers much much better service all around for their passengers.