Facinate is a free
With Facinate, you receive Facebook notifications directly to your home screen via a notification pop-up. Delve into the app itself though, and you'll get access to all of the most important Facebook tools, such as your news feed, messages, photos, etc.
Unlike the official
Facinate is very well designed, with a smart, clean user interface that's very easy to get around. Icons are arranged onto three screens which you can switch between by sliding the screen across.
On the downside, the installation of Facinate takes a long time and the app requests you to grant access to a lot of Facebook permissions, including the ability to add photos, post events, and write on your wall. That's not to say Facinate will definitely do these things, but you need to give it permission to do so nonetheless.
Facinate can also drain your battery life quite quickly, so be careful of leaving it running when you don't really need it.
Facinate isn't quite as well integrated with the Facebook experience as the official app, but it's a very close second, especially as it includes Facebook Chat!