The past few years a trend has grown concerning a startup creating a webapp, paying a staff and priced hosting and yet offering a service for free and with no ads. Sites like droptask, Geeklist, koding and many others are practicing this kind of business and I don't know what are they planning in terms of revenue. There might be a huge interest path I'm not seeing, but it's clearly not obvious. Do you know the paths theses companies are taking to make profit out of those applications?
It's on case by case basis, but I would say that they are trying to build a user base first and monetize later on. Perhaps they have Venture Capital (VC) funding that is keeping them going for the moment.
A prime example of this is Instagram, never made a penny, sold for $1bn, they effectively sold their user base to Facebook.
Tumblr is another great example of this to date its raised $125m of VC funding, and until the last year or so had no solid revenue streams, but what they do have is a great active user base. More recently they have branched out to running targeted ads on their site, only available to larger premium advertisers. According to Quantcast they have around 300M+ page views a day. Now they could easily cake the site in AdSense ads, if they got a CPM of $0.50 they would be generating $150,000 per day (these are very loose workings).
But because of the way that they have taken their time to build a passionate user base, they will now be likely be able to make a much stronger advertising offering.
So the simple answer to your question would be that the sites you gave as examples have funding in place or are bootstrapped and they are playing the long game, trying to develop a maturer company to monetize.
Maybe not yet, I remember when Youtube and Facebook put no ads on their pages and video (pleade CMIIW but at least in my country was).
But there are many ways for startup to pay the bill: donation, pro product, member or page promotion (e.g in your Twitter suggestion, page suggestion).
Money is not always part of the main purpose.
My friend told me that a big company should not take profit from their small project but rather to use their small project to promote their big project. Maybe many big company does.