Tweetbot for iOS
Like many Tapbots apps for iOS, Tweetbot is a beautifully-designed and fully-featured Twitter client for all of your posting needs.

Tweetdeck
If you manage multiple Twitter accounts and need your Twitter dashboard to look like something from NASA, then Tweetdeck should be your go-to client. It allows you to monitor multiple accounts and tweet from any of them with just a few clicks. Tweetdeck for Mac and iOS handles multiple accounts very well.

Echofon
Echofon is another full-featured client that can automatically sync unread tweets between your Mac and iOS devices. Echofon has a great conversation feature that lets you backtrack on all the tweets for a particular conversation. It's available for Mac and iOS.

HootSuite
If you're looking for a Twitter client that also has the ability to schedule tweets, handle multiple accounts, and be hosted in the cloud, then HootSuite is it. It's free, along with a companion iOS app.

Wren
Sometimes, you just want a Twitter client without all the bells and whistles. If you're looking for a Twitter client that tweets without any hassles, then look no further than Wren. It's a simple Twitter app that lets you tweet without any timeline distractions. Post your thoughts or save for later. It's available for Mac.