Great spy movies involve some key aspects of real life espionage: subterfuge, observation, and paranoia. Spies pretend to be alerting they are not, observe their subjects and then act to gather information on their subject or… In some instances, to eliminate their subject. So, using that criteria (entirely defined by yours truly) we can eliminate most of the Bond films (sorry, 007).
I say The Conversation covers the second and third criteria very well, and The Comstant Gardener has aspects of all three. I'd say that Smiley's People is quite good, too.
May I throw a spanner in the works by throwing in the great and classic TV series The Prisoner? The "sequel" to the classic show Secret Agent Man, The Prisoner is a "post-modern" spy show that uses paranoia and spy movie tropes to create a unique and interesting series.