I'd pay a few dollars a month or year in order to: (1) never see ads (promoted tweets, etc.; retweets from channels I follow are ok), and/or (2) premium features like a more sophisticated Twitter iOS app, etc. I'm always surprised by any debate on the web around "OMG how can they monetize? Ads are annoying. Conundrum!" because I thought this was a solved problem in the business domain a long time ago. Identify things people are willing to pay for, and then sell that to them. Those things exist. Do it, rinse, repeat.
Many websites have adopted the donate-to-see-no-ads model - Slashdot, Reddit, OKCupid etc - but as I understand it none of those have exactly thrived on the donated money.