There are several good Facebook clients available in the Android Market. But I would have to say that this is the best I've used so far;
FriendCaster for Android --
It's neat and organized. And it lets you perform FB desktop actions you can't do on the official Facebook for Android app.
This is how FriendCaster's Profile Page looks like. As you can see, there are tabs for Wall, Info, Photos, Albums and Videos, making it easy to access each section. You can also update your status and upload photos and videos with just a few clicks.
Like, Share, Copy or Remove a status update from you or your friends with but a swipe of a finger.
This is the Status Update page. Here you can choose whom you'd like to see your post.
In the News Feed page, you can share, copy, like or comment on posts from your friends with just a few clicks.
Pages sections contains pages you like as well as the ones you manage.
Notifications Section (Amazing as this app is, it's currently not possible to confirm or deny a friend request from within FriendCaster. I hope the developers do something about it soon.)
Compose, Read and Reply to Messages
You can add a message and even tag friends when you check-in
Friends Page shows the profile photos of your friends instead of just their names.
Android's Search hardware button works on the app.
There's even a Favorites Tab where you can add your fave friends and groups and see their updates and uploads instantly.
FriendCaster is currently available for free at the Android Market. Check it out, TP Friends.