Recently there have been several articles by startups who built a service around another company's API, and then got upset that the other company changed their Terms of Service, revoked their API access, or sent them a cease and desist letter. Others have rightly pointed out that Craigslist, Netflix, &c. offer API's to improve the value of their own services, and building a company around access to another's API may be foolhardy.
There's an obvious exception; you rarely hear about terms-of-service or cease-and-desist shenanigans from companies with APIs at their core. Twilio (where I work) is a good example. The amount of money we make is directly correlated to the number of API requests we receive. We have no reason to shut anyone off, because we make more money when people use our API more. Google shut off its Translate API recently, despite a large volume of legitimate use, because it interfered with search quality - spammers were using it to generate thin copies of good content. We would never turn off our API, because it's core to our business.
(One caveat: if your big plan is to use Twilio to spam people, then yeah, we're going to shut you off. We make money when people spend money with us, but we do have an Acceptable Use Policy.)
The only conceivable situation we'd shut down our API is if the company was forced to shut down. That's a risk, but we believe that risk is low and we're working every day to minimize it. So we're not going to shut off your access, unlike Linkedin or Craigslist or another company whose API is a convenience.