As a hacker, for me, the best airline search website would be something that presents all available flights as a gigantic SQL table (or set of tables) so I could just type in a SQL query:
select * from
allflights f
where start = 'London'
and end = 'Chicago'
and roundtrip = true
and airline in ('American', 'Virgin')
etc.
They have an incredibly powerful query language called QPX. Your search would be as follows:
LHR VS,AA ORD (nonstop)
LHR VS,AA+ ORD (zero or more stops)
LHR VS,AA NYC,IAD ORD (with at least one stopover in any NYC airport or at Dulles)
LHR VS NYC AA ORD,MDW (Virgin to NYC, American to ORD or Midway)
LHR F+ ~IAD ORD (any number of legs, but don't stopover at Dulles)
LHR VS ORD / f bc=J|bc=W (nonstop on Virgin in full-fare business class or premium economy)
You can get even more complicated by specifying booking classes, operating airline, specific flight numbers, etc. All this, and it gives you the same time-bar interface as Hipmunk (it's where they got the idea, in fact) which is a fantastic way of visualizing the length of flights, stopovers, different airlines, etc.
For someone who travels a lot (like me) it's indispensable.
The only caveat for me (and this applies to all US-based travel search engines) is the lack of data from low-cost carriers (Southwest, AirAsia, etc) and only Y (full-fare) fare data for many Asian carriers.
select * from allflights f where start = 'London' and end = 'Chicago' and roundtrip = true and airline in ('American', 'Virgin') etc.