The Web spirit of "build an audience and figure out the business model later" is a great filter. It allows products and services into the wild without barriers or the need to sell advertisers on an unproven concept.
Those who can build an audience, such as Twitter and FriendFeed, and before them Google, Facebook, and dozens of others who turned into giants, have the scale to develop monetization schemes that a loyal and fanatic user base won't summarily reject.
In the case of Twitter, the service is a hit, attracting millions of "tweeters," many of whom won't appreciate ads slipped into their Twitter stream.
Here's a solution. How about paying for what you like to use. Much of what gets sent via Twitter is a form of self-advertising. If you like Twitter so much, how about paying $5 a month for the privilege. Of course, the fee would have to include a quality of service guarantee and rebates for downtime. And, you would expect the owners of the Twitter or other services to be priced transparently and competitively, or at least reasonably if no serious competition exists.
In fact, why aren't people willing to pay for what they use? Public radio has the same problem, hence the tedious pledge drives.
A mere $5. Around here, that's less than a day's worth of coffee, a bacon cheeseburger with fries, a lowly beer, and maybe soon a gallon of gas. And you would get unlimited "tweets" and the service doesn't go down, or at least it's up most of the time.
From its inception, the Web has been about free (not like beer) and mostly advertising-supported. You might you say, those $5-per-month fees could add up. You might be paying $25 per month for services you like to use, free of advertising or with ads. Then back off on the steak burritos, country omelets, beet salads, beers, or the bags of popcorn at the movie. The subscription model could work, despite its checkered history.