Twitter users are limited to 1,000 Tweets per day

Update - It's now 2,400 tweets per day (Aug 2014)
"Current Twitter limits
The current technical limits for accounts are:
Direct messages: 250 per day.
Tweets: 1,000 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."
Source:  Twitter Support, retrieved 18th February 2013
Note - Coca Cola were unable to Tweet for 100 minutes during the Super Bowl because they'd gone over their limit