Twitter users are limited to 2,400 tweets per day

"Current Twitter limits
The current technical limits for accounts are:
Direct messages: 250 per day.
Tweets: 2,400 per day. The daily update limit is further broken down into smaller limits for semi-hourly intervals. Retweets are counted as Tweets.
Changes to account email: Four per hour.
Following (daily): The technical follow limit is 1,000 per day. Please note that this is a technical account limit only, and there are additional rules prohibiting aggressive following behavior. Details about following limits and prohibited behavior are on the Follow Limits and Best Practices page.
Following (account-based): Once an account is following 2,000 other users, additional follow attempts are limited by account-specific ratios. The Follow Limits and Best Practices page has more information.
These limits include actions from all devices, including web, mobile, phone, API, etc. API requests from all third-party applications are tracked against the hourly API limit. People who use multiple third-party applications with their account will therefore reach the API limit more quickly. For more information on this topic, please see our API Rate Limiting page.
These limits may be temporarily reduced during periods of heavy site usage. In such cases, we will post an update on the Twitter Status blog."
Source:  Twitter Support, retrieved 11th August2014
Note - in Feb 2013 it was only 1,000 tweets per day