You will find that most stations were actually cut-and-cover, with only the Red Line having bored segments: one starting from after Farragut North [2] and running until shortly after the Medical Center [3], and another starting as soon as it leaves the CSX Metropolitan Sub northwest of Silver Spring and continues until the terminus at Glenmont, although that station itself was built from the surface [4].
Also highly recommend the book 'The Great Society Subway: A History of the Washington Metro' [5]
[1] https://www.washingtonpost.com/graphics/local/wmata-metro-de... [2] http://www.johnreilly.us/washington-metro-transit-design-and... [3] http://www.roadstothefuture.com/Metro_Glenmont_Route.html [4] http://www.nycsubway.org/wiki/Washington,_D.C. [5] https://books.google.com/books?id=beDoAwAAQBAJ
Some NYC subway stations and lines were built with boring as opposed to cut and cover. 90% of the new 2nd Avenue line, for example, is planned to be bored[1]. Here[2] is an article with more details about the tunnel boring machine used -- the comments also have a lot of good discussion. Also, Los Angeles has done some boring for its new subway lines[3].
1: https://en.wikipedia.org/wiki/Second_Avenue_Subway#Construct...
2: http://secondavenuesagas.com/2010/05/14/down-the-rabbit-hole...
3: https://www.metro.net/projects/tunnel-boring-machine-tbm/