The score for the 1974 adaptation of Agatha Christie's novel was composed by Richard Rodney Bennett. It is generally characteristic of Bennett's compositional style -- a blend of classical and jazz influences. He also used elements of music from the 1920s and 30s (the time period in which the story is set) to make the score seem more 'accurate.'

The Main Theme of Murder on the Orient Express

The film's main theme, a waltz in the Austrian-Hungarian style, is not played over the opening credits. It is not heard until the main characters have been introduced and have each boarded the famed Orient Express and the train starts moving. Something about the piece's triple meter time blends exceptionally well with the visuals of the train as it begins to slowly creep along the track. The waltz gains momentum as the train gains momentum; the visuals and the soundtrack line up perfectly. The waltz is arranged for and played by a full orchestra; the main melody is played first by the woodwinds and then by the strings, and accented by the woodwinds.

The waltz's introduction is repeated at several points during the film, including the points during which the train is stuck in a snowdrift. It doesn't progress into the full waltz during these parts, however, since the main section of the waltz is meant to represent the train's movement and it isn't moving. The waltz is also repeated over the film's closing credits as the train continues its trek through the European landscape. It is during the closing credits that we hear the waltz in its entirety, including its conclusion; the coda consists of a spiral of descending notes.

Foreshadowing in the opening credits

The music in the opening credits is a jazz-influenced piano piece. Some have referred to it as being in the concerto style, as the piano may be considered the solo instrument that is accentuated by the orchestra. The overall elegant tone of the credits is amplified by the music, which is cool and unassuming. This contrasts with the serious themes present throughout the rest of the film.

The most remarkable thing about this sequence is its timing. Though the majority of the music is calm and cool, it reaches a climactic crescendo and plays a minor chord when Richard Widmark's name is on the screen. Widmark plays the man who is murdered during the film. The contrast makes it impossible to not notice the difference, and this alerts viewers to the idea that Widmark's character may be extremely important to the plot.

The flashback sequence

A central part of Murder on the Orient Express' plot involves a murder that took place several years before the film's main events. The film begins with a recap of these events so that the viewers will better understand certain issues later on. The recap tells the story of a young girl who was kidnapped and held for ransom; once her family paid the ransom her body was found. The music in this section of the film evokes a mysterious and suspenseful mood through repeated use of "crying" sounds by the strings in their high register.

Bennett also makes this phrase a leitmotif; he uses extremely similar musical techniques in other scenes that have similar themes. The motif is repeated after the murder on the train as Hercule Poirot ties the original murder in with the 'current' one. Similar instrumentation and orchestration is also used as the viewers see a 're-enactment' of Poirot's solution of the case.

Leitmotif

While several characters have their own leitmotifs, the only character with a major theme of his or her own on the soundtrack is the Princess Dragomiroff. This may be because her interrogation is not part of the main interrogation sequence and takes place in her bed chamber (the rest take place in the main part of the train's coach). Her music is also somewhat more elegant and stately due to her status and position. Bennett also uses the instrument-matching technique (see Peter and the Wolf) at several points during the score; phrases similar to those used in the opening credits theme are sometimes played by woodwinds as Poirot searches the train for clues.
I've seen the movie several times. A soundtrack exists but I don't own it. Other research about Richard Rodney Bennet was conducted at places like Wikipedia and several biographical sites like http://www.schirmer.com/composers/bennett/bio.html.