There's not much you can do about Twitter's promoted tweets, as annoying as they can be, but the service has to make a buck somehow. Fortunately, you can now restrict the information the social media site uses to cater the ads to your interests, adding a little more privacy to your browsing experience.
gHacks' Martin Brinkmann writes about the introduction of the new options, which can be found in Settings -> Account section. The ones you want to uncheck are "Tailor Twitter based on my recent website visits" and "Tailor ads based on information shared by ad partners".
For the curious, Twitter has an FAQ up, if you'd like to know more about how the ad tailoring works. It's worth a quick read — this part in particular makes it clear that, even with these options disabled, your Twitter interactions will still be used for targeted advertising:
If I uncheck my "Promoted content" setting, am I opting out of all Twitter Ads and all ad customization? No, you won't be able to opt out of seeing ads altogether. When you uncheck the "Promoted content" setting, the ads you see may still be customized for you based on what you do on Twitter, including the messages you tweet, the people you follow, and the links you click on Twitter. But your account will not be matched to information shared by our ad partners for tailoring ads, and the ads you see may become less relevant.