I think this is a loaded question? You need to ask more pointed and thought producing questions to get the answers you are seeking? Like in what class of service, routes, carriers types, charter, full service, LCC's? See what I mean to many variables here.
On the whole European airlines offer the best service with complimentary alchohol still being served even on domestic flights (e.g. BA & BD), in economy. The BA inflight food on short flights is miles better than BD. On the other and there are exceptions for example Midwest in the US.
The best overall service I ever had, from check in to claiming my baggage, was on a Canadian Airlines flight from YXE to YVR connecting to SFO in 1999. Everyone working that day were ALL in great moods and everyone just lightened up a bit and had some fun.
Luv2fly is right that the question is a bit ambiguous. however, it's still fun to talk about what are favorites are.
i would have to agree with shamrock 747: virgin atlantic coach is the best. however, as of january 3, 2003, i would say air france has the best business class. i know that a lot of the transatlantic carriers have been adapting their services, so it's possible ba has pulled ahead.