Lolita
Although this may not seem like a road movie at first glance, Lolita is definitely my favorite road movie for several reasons. Firstly, the unsettling relationship between Hubert and Lolita strays from the typical pairing of two people setting out on the road. Secondly, their experience is one of seeking freedom, because they must shed the social stigma of their difference in age, but also of imprisonment, because Lolita is under the control of Hubert.
Also, the road both brings the couple together and tears them apart. While driving, they are followed, which unites them together in fear of being discovered, and necessity to keep moving. However, once Lolita realizes that Hubert has lied about her mother and he becomes increasingly more controlling, their relationship begins to deteriorate. The viewer watches Hubert slowly lose the trust he built in Lolita, and he drives furiously onward, trying to repair it. Furthermore, the trip permeates the rest of their lives because people they meet on the road also decide their fate later on. The two meet a man named Clare Quilty, whose involvement in Hubert and Lolita's life does not remain isolated to their confrontation on the road. When they meet again, the results are violent (but I wont ruin it for those who haven't seen it).
What I like most is the way in which driving is both a means of escape, and a damning and detrimental environment to the couple...both the solution and agitator of their problems.