How many Apple IDs should one household have?
There is no limit and having more is not necessarily better. Having all your devices registered under one Apple ID has the benefit of having all your purchases pushed to them without having to manage multiple accounts. So your wife can enjoy an app on her iPhone 4 just the same as you can enjoy the same app on your iPad 2, without needing to purchase the app a second time (once for each device), or constantly logging in and out of various Apple IDs to install and update.

I find it is always better to pool your purchases to one account and register your devices under that single account. Having multiple Apple IDs requires that one micro-manage each account (iTunes will only check for updates for the current Apple ID), which can be bothersome at the best of times and a nightmare at the worst of times.

One advantage of having separate Apple IDs, however, is that each account belongs to its respective owner and can be registered to their own payment methods. But if you share your finances, that is of little value to you.

iCloud is bound to its respective Apple ID, so if you have just the one, all the features of iCloud would permeate through any device registered to that account. That means if you downloaded an app on your iPad 2, it would appear on your wife's iPhone 4. You would also share documents, pictures, music, etc. (anything supported by iCloud and expressly enabled by you) across all your devices as well—email as well. iCloud would essentially unify them and their content.

Multiple Apple IDs are not required. You may also find this article on managing multiple devices (although somewhat dated when iCloud launches).