A syntactician "must-read" list

I agree with Greg Lee that McCawley is the place to go for the canonical generative treatment of English syntax and that GPSG is the generative counterpart to that. However, things have moved on since then. I would further recommend looking into Unification Grammars (which is very much at the heart of minimalism under a different name) and Construction Grammars.

For the former, I recommend starting with Ivan Sag et al.'s Unification and Grammatical Theory. And my personal bible on construction grammar is William Croft's Radical Construction Grammar: Syntactic Theory in Typological Perspective but Adele Goldberg's Constructions are also a good introduction. Of course, Fillmore's work on this was very foundational and elucidates the initial motivations behind the construction movement. Croft does a very good job in the introductory chapter of setting out the construction grammar space and its relationship to kindred frameworks such as the Lexical Functional Grammar.

What you will find with construction grammar is that many of the problems that the generativist frameworks deal with simply disappear as syntax and semantics are brought closer together. I think Langacker is the best author in this respect.

However, you should also not skip dependency grammars if you want to get a comprehensive view of syntactic theory. The work of Sgall and Hajicova (full disclosure - both were my teachers) has been leading the way in recent decades (e.g. with this recent publication). This work will also highlight the importance of information structure or topic-focus articulation (something none of the other frameworks are concerned with - except perhaps in a round about way construction grammar).

This is still a very selective overview, there are dozens of grammatical frameworks within these broad trends: generative (constituency), generative (dependency), constructional. With many more cutting across such as unification or information structure. You could spend a lifetime cataloging them. But I think the reading list above might give you a sense of the scope of the project.

Update
Tim Osborne reminded me in the comments that Lucien Tesniere's "Elements of Structural Syntax" is now available in English translation, so that should definitely go on the list. He is the foundation on which all later dependency grammar frameworks explicitly build.

This also reminded me that Jan Firbas' Functional Sentence Perspective in Written and Spoken Communication would make for a great introduction to information structure.