Luke Timothy Johnson, in The Creed, says that reciting the creed—he means the Nicene Creed, but I think it works for the Apostles’ Creed or others as well—is a counter-cultural act. What is being done when the creed is recited:
In a world that celebrates individuality, they are actually doing something together. In an age that avoids commitment, they pledge themselves to a set of convictions and thereby to each other. In a culture that rewards novelty and creativity, they use words written by others long ago. In a society where accepted wisdom changes by the minute, they claim that some truths are so critical that they must be repeated over and over again. In a throwaway, consumerist world, they accept, preserve, and continue tradition. Reciting the creed at worship is thus a counter-cultural act. (40)
That’s not to say that churches need to be counter-cultural for the sake of being counter-cultural. However, the gospel is itself counter-cultural and yet the church is often pro-cultural—and often subconsciously so—so to be consciously counter-cultural in our worship serves as a good reminder about where our allegiances lie.
Some people are uncomfortable with certain aspects of the creeds—say, the virgin birth—that they may be reluctant to recite it, thinking that doing so would lack integrity. Justo Gonzalez, writing about the Apostles’ Creed in The Apostles’ Creed for Today, has this to say in response:
…think of the creed not so much as a personal statement of faith but rather as a statement of what it is that makes the church the church, and of our allegiance to the essence of the gospel and therefore to the church that proclaims it. (7)
To recite the creed with that in mind is also a counter-cultural act.
[Added: I'm reading up a bit on the ecumenical creeds of the church for a small group discussing the basics or essentials of faith. We don't recite the creed (or at least we haven't in my time) at our church and our denomination is "non-creedal" while still affirming the major ecumenical creeds, but these writers make a convincing case!]