In Shakespeare's Hamlet, Act One does not just introduce the characters to the audience; it also concentrates a great deal on the theme of family. And much of what occurs in the first act reflects the same kind of family dynamics we see in the present-day world.
There are many present-day concerns in this early 17th Century drama. Hamlet has lost his father. Based upon social proprieties of the day, Hamlet's mother remarries too quickly. Hamlet is embarrassed by her behavior, telling Horatio sarcastically that food from the funeral would still have been fresh enough to serve for the wedding because the one followed so closely after the other:
Thrift, thrift, Horatio. The funeral baked meats
Did coldly furnish forth the marriage tables. (I.ii.185-186)
Hamlet resents his mother's hasty remarriage (within one month of his father's death) and the foolish way she acts with her new husband (like they are young newlyweds). He is furious when Claudius and Gertrude also advise him to move on with his life and get over his father's death.
Good Hamlet, cast thy nighted color off,
And let thine eye look like a friend on Denmark.
Do not for ever with thy vailed lids
Seek for thy noble father in the dust. (I.ii.70-73)
Then Claudius chides Hamlet, saying he shows stubbornness, unmanliness, disrespect and a poor understanding of the Church and its view of death in general—in so long mourning his father. This can only make Hamlet furious—for regardless of Gertrude and Claudius' hasty marriage, Hamlet knows that his grief is sincere and impossible to deny. As with blended families today, Hamlet and the rest of his "family" are struggling to find a balance. His stepfather shows little understanding of his stepson.
In scene two, Polonius meets with his son, Laertes, as the young man prepares to return to Paris: he had only come home for Claudius' coronation. As would a father in a more modern setting, Polonius gives his son advice about how to act while he is away—not to borrow or lend money (among other things) and to be honest with himself, and therefore, also with others.
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man. (83-85)
Laertes also warns Ophelia to watch her step with Hamlet: because Hamlet is required to marry as befits his position as the Prince of Denmark...
He may not, as unvalued persons do,
Carve for himself; for on his choice depends
The safety and health of this whole state... (22-24)
Laertes suspects (incorrectly it seems) that Hamlet is only having a dalliance with Ophelia, for Hamlet would never be allowed to marry Ophelia. These dynamics are typical of those today between members of a family: the parent worrying over the children and/or a brother concerned for his sister's happiness and reputation.
While we cannot be certain about the existence of ghosts (as when Hamlet seems to meet the ghost of his dad), Hamlet does learn of his uncle's treachery...of his father's murder. And while it may not be common today for one man to murder another to steal his throne, it is typical today that a young man who is resentful of a new stepparent would not be reticent to believe the worst of that person.
Many of the dynamics in the play take place because of family—and between family members. In terms of this theme (along with many other elements), the dynamics in the play coincide with the present-day—making it timeless.