Twitter offers a rich API allowing applications to perform nearly every action with bots that can be done on the Twitter website.  Here are a list of actions that you can perform with Twitter bots and some possible use cases.

Bots ActionAction DescriptionNotes / Use Case
Send Public ReplyAuto reply to tweets that contain particular words or match a certain criteriaIf a tweet includes your brand mention, you can send a canned auto response to the Twitter user.
Send Private DMSend a Direct Message to people who have tweeted on certain topicYou can send DMs to people who follow you or those have chosen to accept DMs from everyone.
Retweet TweetRetweets a public tweetIt is similar to hitting the retweet button against a tweet on the Twitter website or mobile app.
Favorite TweetFavorite a public tweetTwitter policy team has requested us to remove the auto-favorite feature from bot.
Quote TweetRetweets a tweets but prefix the tweet with your own comment (RT + Comment)If @user tweets “what is the color”, your bot can tweet “Blue RT @user what is the color” to give context to the reply.
Follow TweeterFollow Twitter users who have tweeted on specific topicsAuto follow twitter users who tweet about your brand or your favorite sports team.
Add Tweeter to ListAdd Twitter the user to an existing listMake a Twitter list of people who tweet about your brand. A list can have no more than 5000 members.
Follow ProfileSearch Twitter profiles by full name, company name, location, or other criteria.Auto Follow profile that match your criteria.
Add Profile to ListAdd Twitter users to a ListSearch Twitter profiles and add them to a list. For instance, you can build a list of all profiles that have your company name in the bio / description.
Follow BackFollow someone who follows another userIf @user gets a new follower, follow back
DM FollowersSend a message to your new followersYou can DM anyone who follows your Twitter account.
Add Followers to ListAdd followers of any user to a Twitter listIf @user follows @someone, automatically add them to your Twitter list