Trust and Sorrow
Christians don't make the Stations of the Cross out of sentiment or nostalgia. They make it because the very definition of "Christian" calls for it. To be a Christian means, not to just believe in Christ's teachings, but to dwell in Christ - to take on the mind of Christ. As Paul says, "I have been crucified with Christ; it is no longer I who live, but Christ who lives in me…" (Galatians 2:20).
Everything about the Christian life - the sacraments, personal devotion, sacrificial love and charity - is rooted in Christ, empowered by him, and directed to him.
So when Christians make the journey of the Stations of the Cross, they are simply making that Christian journey in a very vivid and specific way. In gratitude, in sorrow for sin, - we die with Christ, trusting that we will, with him, live.