Only iTunes running on a computer can be authorized to use more than one Apple ID. I don't know what the limit is if there is one.
iOS devices* can only be configured to use one Apple ID for use with the iTunes Store. (However, a separate Apple ID can be used for iCloud services like mail, calendar, contacts etc., but that is a separate issue.)
Home Sharing can only be configured to use one Apple ID at a time so if you want to use Home Sharing to connect an iOS device to an iTunes library or to connect multiple computers to an iTunes library you can only do it with one Apple ID.
So, with all that in mind, yes you can create separate Apple IDs for everyone but it will affect what you can do with the apps and media you purchase from iTunes. If everyone shares a family account then there will be no restriction on who can play, install or share the media or apps. If you create separate accounts there will be restrictions on what can be shared or installed on the various devices.
A family will benefit from sharing a family account that everyone has access to. If you have parental concerns about restricting access to certain apps/media for younger children than a separate account shared by the children may be the answer.
*iOS devices are iPod Touchs, iPads, iPhones and Apple TVs.