I've read more than once that Twitter doesn't have a follow limit, but today has proven otherwise. After about 1000 follows or so, I received this message:
It looks like you've hit a following limit.Learn more
The 'Learn more' links to a 'Follow Limits' page vaguely explains that there are limits created to protect the system from spammers. The official technical twitter follow limit is 1000 follows per day, and this is based on a ratio of followers to followers.
Aggressively following users it prohibited
From what I can tell, You're allowed to follow as many people as you want until you hit the limit determined by your follower to follower ratio. Your only choice if you want to follow new users at this point is to unfollow old user to follow the new one. Twitter seems to lose its patience if you unfollow and follow large amounts of user to "aggressively" and labels this behavior as 'Aggressive Follow Churn'. Twitter will ban accounts they think are performing 'aggressive follow Churn'.
For more information on the 'it looks like you've hit a following limit' error visit: following rules and best practices