Should Christians visit the cemetery?
I think all of us would attend the funeral of a friend or loved one, so I assume this question is not about that practice. It is customary to attend a funeral ceremony to acknowledge the life of the person who has recently departed. Such a ceremony is a good place to remember the life of the person and to minister a word of encouragement (1 Thess. 4:13, 18) and to remind those attending of the shortness of life and the importance of receiving and serving the Savior (2 Cor. 6:2). Also, I cannot answer for cultures other than my own Western culture. It may be the case that there are cultures where it would be inadvisable for a Christian to visit a cemetery.
The question seems to be about the practice of repeatedly visiting the grave of someone who was important to the visitor. I think we must recognize that there may be various motives for such a visit. We must also consider the effect such a visit might have on others. These are not always easy to determine and absolute judgment as to the propriety of such visits really must depend on the individual situation and conscience. So, here I cannot suggest any rules, only make some observations.
First, what is the reason for the visits? The visits might be to show respect for the person who lived. Maybe it is to provide a time to grieve (Jn. 11:31). Perhaps it is an occasion for parents to share encouraging stories about their relatives and share the gospel and the hope of being reunited. It is interesting that it was the women who visited the tomb of Jesus while the men were (apparently) hiding with doors locked (Jn. 20:19). The affection being shown cannot be denied and they received the proclamation “He has risen; He is not here” (Mk. 16:6). So, a visit might be used as a reminder of the glorious day of resurrection.
On the other hand, if the visit is clouded with sadness or even mystical thoughts (which would be worse) then such a visit must be discouraged. One might visit a gravesite thinking to give or receive some kind of message from the dead. A believer should not fall into such a mistake. Sometimes in our grief, we can easily forget the blessedness of knowing a loved one is “with the Lord.” (2 Cor. 5:8) Certainly, there should be no thought of having an effect on the state of one who has died, such as praying so that they move from “Purgatory” to Heaven. Regrettably, this error is taught in some branches of Christianity.
Finally, and above all, we must remember that our bodies are simply “jars of clay” (2 Cor. 4:7) and that the person (if a believer) is in paradise (Lk. 23:43). We might remember them as they were but that is not how they will be. We will be reunited and in a glorified condition. This is what should be uppermost in our thoughts regardless of whether we visit the gravesite or not. I do think that the pictures and videos we have taken of the good times with friends and relatives replace much of the reason for gravesite visits.