I'm posting an update to my own post after a few days of working with this. The Apple ID is used in many, many places, and I start by listing them all here to define the scope of the problem. At the end, I detail how we are currently set up and what is working well after a few days of use.
iBooks - keys off what is set for Settings->Store. This affects book synchronization and must be different for two people reading the same book that each has more than one device (e.g., an iPad and iPhone) that they want to stay in sync. This is one of the biggest problems in my house because we want to stay configured on the same "Store" account so that all purchases go through one account and are available to everyone, but we often read the same books and don't want one's reading to flip pages for the other when a sync of bookmarks occurs. We also don't want to turn off syncing because we both have multiple devices and we want syncing to happen between our individual iPhones and iPads.
FaceTime - set in Settings->FaceTime. Typically each user will want to get FaceTime calls at a separate "address". You have two choices. You can use the same Apple ID and configure FaceTime to respond at different email addresses, or you can use separate Apple IDs and there is no conflict at all. For an iPhone you will already have separate phone numbers, but for an iPad people will use an email address to FaceTime with you, so the email addresses you use have to be different.
iMessage - set in Settings->Messages. This is almost identical to FaceTime. You have to provide an Apple ID, but you can distinguish different users based on email addresses.
App Store - set in Settings->Store. The Apple ID used here is what is used for purchases. This applies not just to purchases when you're in the App Store application, but also any in-app purchases, any bookstore purchases via the "Store" button in iBooks, any purchases in the iTunes app, and purchases from the "Store" button in Newsstand.
iCloud - set in Settings->iCloud. Defines one fixed set of storage, mailbox, calendar, contacts, and Find My iPhone. I'm going to split this up and talk about each area separately below. The main choice here is whether two people should share an iCloud account or should have individual ones. In addition, some people have proposed creating a third "family" iCloud account for sharing some information. Much of what could be done with a family account could be done by adding each person's individual iCloud account to all devices, so I don't treat that separately here. In addition to the reasons below, one good reason for having separate iCloud IDs is that you each get 5GB of free storage.
- Mail - I don't know anyone that wants to share mail in a household, so this probably isn't a big problem and using separate Apple IDs is probably acceptable here. For someone that wants to share this much, they would probably just all use one Apple ID anyway.
- Calendar - iCloud actually has calendar sharing, it's just only available on the web as far as I have found. If you log in to your account at icloud.com, go to the Calendar, and click one of the little icons on each calendar's name, you can share that calendar. My wife and I have decided to make her calendar the "main" one, and she shares it to me for viewing and editing. I can then view it on my iPhone and iPad even though I used my own Apple ID to configure iCloud. When I go to the Calendar App and select the Calendars button in the upper left, her shared calendar is listed with "Shared by <wife's name>" under it. Pretty slick.
- Contacts - I wish iCloud allowed sharing contacts in the exact same way it shares calendars, but so far as I know it doesn't yet. The best solution for now seems to be to add my wife's iCloud account as a secondary iCloud account on my devices, and turn off everything except Contacts. There may be some downsides to this as secondary iCloud accounts on a device do not use push notifications. This may mean that contacts only get updated when I open them individually or open the Contacts app, for example, this needs further verification. We've just decided to not share contacts for the time being.
- Find My iPhone/iPad - If two related people have separate accounts for this, then they cannot see all of their devices in one place in Find My Phone. They can know both Apple IDs and passwords and log into Find My Phone with the appropriate set of credentials to see a particular device. For example, if I want to find my iPhone or iPad I log in with my Apple ID, and if I want to find my wife's iPhone or iPad, I log in with her ID. I have found the Find My Friends app to be a good replacement for this, but it is a different feature in that it follows a "person" and not a "device". My wife configures whether her friends are following her iPhone or her iPad, and whereas Find My Phone can find her with either, Find My Friends requires that she be carrying the right device to be useful. She almost always has her phone, so this is a satisfactory switch. This may have other disadvantages though. For example, if she ever hides her location in Find My Friends from her other friends (this is a switch you can turn on and off when you want privacy), she will also prevent me from finding her. That may be her intent :), but Find My Phone wouldn't ever allow that. We have found that Find My Phone avoids a lot of the "are you almost home" calls to each other. Find My Friends looks like it will offer a lot more features and be better for that rather than misusing Find My Phone the way we were before.
- Photo Stream - I currently have no good solution for photo stream. From Apple's support documents it appears that the secondary iCloud account solution would not work, but I have not tried it. For now I simply am not using it. I sync all of our photos to a PC, then back out to each device once a week. The PC also uses home sharing through iTunes to share with an Apple Tv. I would still have to do this anyway as Photo Stream is only for storing your last 1,000 photos and as such isn't very useful to me (we have over 12,000 photos since my kids were born 4 years ago).
- Other Cloud Data - iCloud is storing a lot of other data, like bookmarks, that two people may or may not want to share. In my case, my wife and I visit pretty different websites, so we don't want to share bookmarks. We also don't want to share Notes or Reminders, so this works out good. If we did want to share these, then adding a secondary iCloud account would probably be the best solution.
Apple could do a few things that would almost completely alleviate my current problems. First, allow specifying a separate ID in iBooks for the purpose of page/bookmark syncing. I may want my wife and me to purchase books on the same account, but I want to separate our syncing of bookmarks. Second, if iCloud Contacts had a sharing feature just like iCloud calendars do, we would be in good shape with contacts. We have a very similar set of contacts, and we have no desire to maintain them separately. Third, allow inviting others to a Photo Stream much like Find My Friends. Then our whole family could share one Photo Stream.
So in the end this is how we have our devices configured:
1) We each have a separate iCloud account (i.e., we use our individual Apple IDs for this), and only one iCloud account is configured for each device. This means that we each get our own mail, contacts, calendars, bookmarks, and Find My Phone. My wife shares her calendar to me so that shows up in my iCloud account (you can do this from the web on icloud.com). The only downside I have noticed is that we do not currently share contacts in any way and we would like to, but we could do this by one of us adding the other's iCloud account as a secondary account on our devices. For some reason I just don't like that solution and am avoiding the secondary account. We also do not use Photo Stream yet.
2) We share one Apple ID for all purchases. This is okay most of the time, but is a pain for iBooks as noted above. What often happens is my wife signs out of my Apple ID and logs into her own if she will be using iBooks, but then she has to switch back again whenever she makes any purchases (including in-app purchases).
3) For FaceTime and iMessage we happen to use separate Apple IDs, but it is the email addresses that matter so this isn't significant as far as I can tell. For a household sharing an email address, you might prefer separate Apple IDs for this.
4) My kids do not yet use email or any of the iCloud features other than Find My iPhone (which really I use on their behalf in case their devices get lost). So for now iCloud for them uses my Apple ID just for Find My Phone, and the other services are disabled. We have their restrictions (under Settings->General->Restrictions) locked down so they do not have access to Safari, the App Store, iTunes, or FaceTime. Thus, they don't have any bookmarks to sync or other services to configure. The biggest pain point for them will be when they start reading more (they are currently 2 and 4) if iBooks continues to leverage the App Store account for bookmark syncing. Even then it will only be a problem if we all read the same book at the same time, which is less likely than it is between my wife and me. Once they are old enough for their own email we should be able to repeat the above to give them their own iCloud accounts. We will then all likely share mom's calendar for family events (perhaps in addition to individual calendars), and we will all add each other in Find My Friends.