Desktop recs
One of many Twitter applications available for free, and very popular with educators. Has web-based version. Allows tweets to be scheduled.
Convenient way to monitor and participate in twitter chats. Appends the hashtag automatically. Alternative to Tweetchat (which no longer works).
Schedule your tweets so that they go out at fixed times.
Link your Twitter account to it so that all retweeted and favourited links get automatically bookmarked.
Android recs
My favourite app for Android. Good one for power-users. Tablet-optimised.
iOS recs