I find that there is a crossover of music that is put under the umbrella of 'Ambient' and it can mean many different things to different people. Balearic Chillout, Muzak, Minimalism, Krautrock and even Prog Rock could all be classed as one form of Ambient or another.
Personally I don't think that any one particular genre is more relevant than another and although in the true sense of the term Ambient suggests to most a steady and stable sound that eschews rhythm and instead relies on monotony, in pure listening terms I am in the camp of those that get the maximum enjoyment from laid back sounds no matter what genre they come from.
So ALL these songs are Ambient to me:
Kudos to the Stars Of The Lid mentions. They occupy the minimalistic side of Ambient but hold the attention beautifully if you are in the mood for such a stripped down sound.
Probably the finest of early 20th century composers that fit the bill:
I could throw out names like Steve Reich, Rhys Chatham, The Field etc but I am sure many people know about them too and that their music is so pure that we may fall asleep
I am a fan but a snippet of Chatham is not the best convincer in the short term.