Non-denoms really are an extremely varied bunch. On the one hand, you have the “mega-churches,” many of which are non-denominational but some of which are affiliated with various denominations. In those cases, though, they tend to act very independently and play down denominational affiliation (though not always). Megachurches are predicated on a rather utilitarian model of church, IMHO. They have multiple services every week, structured so that everyone can find their “niche.” They tend to focus on evangelism of unbelievers and instruction of believers rather than on simply worshipping God (indeed, a proponent of this model would probably find my assumption that one can “simply worship God” to be narcissistic, naive, and reflective of some kind of heretical notion that God needs something from us). In these churches, the primary sense of identity often resides in small groups which meet at some point during the week. Thus, in spite of their huge size, megachurches have a very strong sense of community and (when it works right) everyone feels like they belong. Don’t scoff at this–I think it’s far more important than Catholics generally recognize. Megachurches usually are conservative in their doctrinal and moral teaching, but on the whole emphasize discipleship and practical Christian living rather than the finer points of theology. They thus tend to be fairly open and ecumenical–few megachurches would say that “Catholics are not Christians,” for instance, though they might regard Catholicism as very bad at teaching people and bringing them into a living relationship with God. Some megachurches do focus heavily on the pastor, who however is seen more as a manager and facilitator than as a priest or prophet. This can lead to a personality cult, or in other cases it can lead to a deemphasis on the pastor and a genuine attempt to develop everyone’s gifts, so that leadership is distributed widely. Also, megachurches have a large staff, so there isn’t going to be one single pastor to focus on, although the senior pastor may be a very strong and colorful personality and that’s when “personality cults” can develop.
Then you have the small fundamentalist “store-front churches,” which are at the opposite end from megachurches. Again, these may be affiliated with a denomination or loose fellowship of congregations, but if so it will be a small, conservative group, not one of the “mainline” denominations. These churches focus tightly on toeing the line, both doctrinally and morally. They require a very high level of commitment and members usually feel very close to each other. They tend to condemn both the Catholic Church and “mainline” Protestant churches as apostate or at least lukewarm. These churches often (but not always) have a very authoritarian model, with the pastor seen as the “man of God,” basically a prophet-figure who must be listened to.
Then you have house churches–groups of people who meet in living rooms for worship. These tend to have the pragmatism and unconventionality of the megachurches combined with the rather suspicious attitude toward the outside world characteristic of the more fundamentalist congregations. Typically house churches are the most anti-traditional of all non-denominational groups, and often see all official churches as having fallen away to some degree or another. They tend to be extremely egalitarian, at least in principle (and at least among males–the role of women varies). Many house churches are charismatic, but many others are not.
This is a very broad portrayal of three kinds of non-denominational churches I’ve observed. A lot more could be said, and most o fmy generalizations could be challenged. But hopefully this gives some food for thought.