Turkish Prime Minister Tayyip Erdoğan announced that the courts have ordered Twitter be blocked completely.
This appears to be in response to Twitter refusing to take down tweets of audio recordings purporting to be of Erdoğan engaging in corrupt activities.
Twitter is suggesting that users fall back to an SMS interface to continue to access the service. I suspect most active Twitter users follow enough people that the feed would overwhelm their SMS plans completely.
A better solution is to use a VPN like Anonymizer Universal to punch a hole through the censorship. Through Anonymizer you would then be able to access Twitter, or any other website the Turkish government might be trying to block.
Update: We have re-confirmed that Anonymizer is still accessible and working from Turkey.