Doppelgangers
A doppelganger in the technical sense is the double of oneself to whom one is not related. It can also be termed "twin strangers". However, in Strangers on a Train, Hitchcock explores the theme of psychological, rather than physical, doppelgangers in his two main characters, Guy Haines and Bruno Anthony. They are emotional mirrors of each other, although not mental ones, given that Bruno is a psychopath, but Guy is not. The two men share the same dark longing for the death of a thorn in their respective sides; Guy wants Miriam murdered just as much as Bruno wants his father killed, even though the plan stems from Bruno's imagination and not Guy's.
Bruno is also Guy's darker doppelganger in that he is the living embodiment of Guy's secret fantasy of killing Miriam and having her disappear from his life forever.
Everything in Twos
Hitchcock was fastidious about the theme of doubles in the movie and sets this in stone very early in the movie when pairs of objects are presented to the audience. There are two sets of train tracks that cross each other; two taxis, two double liquor beverages ordered by Bruno. Hitchcock himself is seen on screen carrying a double bass. The purpose of this is to remind the audience of the two men doing different things, in different places, at the same time, but in a coordinated attempt at seeming independent they only serve to remind us that they are working in tandem with each other.
Duality of Character
Hitchcock loved to present the theme of darkness and light within the same person and at first glance it would seem that Guy is the "good guy" in the movie, and Bruno the bad. However, when looked at again more closely, Bruno can be seen to be the darker side of Guy's character and he also explains the duality of character that make Guy appear to be the perfect, all-American preppy boy next door, whilst simultaneously helping to facilitate the brutal murder of his wife because she will not give him a divorce.