TweetDeck has always been my personal Twitter app of choice. Even though heavy Twitter users will argue it isn't as robust as some other apps and can be a little bloated, I find it to be the best for my situation.
The app has recently been released for Android and includes many of the features TweetDeck users have come to expect. The app actually comes close to matching its desktop counterpart and offers some of the newer integration options for Facebook, Buzz and Foursquare. The app is extremely easy to use and still holds the bar for my favorite app.
The best part about this app is that it is free, which is amazing for how robust it is. It still allows for geotagging, trending topics and many more popular features. The interface takes some time to get used to, but once you get the hang of it, it is definitely the go-to app on Android. The developers promise many more features like real-time visualizations and seem to plan on updating it frequently.
This app is definitely worth looking into and I'd recommend it for anyone who uses Twitter. Check it out.