Twitter's a great way to monitor breaking news and quickly connect with others in 140 characters or less, but the company's latest efforts have been to monetize the service with promoted content and ads and also make Twitter feeds more of a personalized experience, a la Facebook. There are a few things you can do to control your privacy.
Security solutions provider F-Secure suggests unchecking all the three options at the bottom of your Twitter account's security and privacy settings if you're concerned about maximum privacy: Discoverability, Personalization, and Promoted content. These let others find you by email (if you gave Twitter your phone number, there's also an option for being found by phone number), track your website visits to tailor Twitter content, and display ads based on information advertisers may have on you (based on your previous visits to the advertisers' sites or reading their newsletters).
In addition to those basic settings, which you might have seen before, now there's an opt-out option for the Twitter iPhone and Android apps. Unless you opt-out, Twitter will collect data on the apps you have installed and are using...again, in order to personalize your experience.
I'm all for personalized experiences, but privacy shouldn't be opt-out, it should be opt-in.