It's perhaps ironic that, having read all of the Ripley novels years ago and loved them, that I would only now get around to reading (listening, actually) to Strangers on a Train. The basic plot must, by now, be well-known to just about everyone. For the three of you who don't know the story, two men meet while having drinks on a train and discuss their respective complaints about Bruno's father and Guy's ex-wife, both of whom are making their respective lives miserable.
Bruno, hatches a one-sided plan for each of them to commit the perfect murder by having each one take care of the other's problem. Guy, an up-and-coming architect with a new girl friend wants nothing to do with the crazy idea. Bruno assumes it's a deal and eliminates Miriam, Guy's ex. He then begins to hound Guy to fulfill the other side of the "bargain."
The suspense comes from watching the effect on Guy of Bruno's incessant badgering for him to complete his end of the "bargain." As others have noted, this is not your standard mystery, but it's a marvelous "why done it," and examination of the human mind's capacity for guilt and evil.