This problem came out of a recent project I was working on. I had to perform a bunch of API lookups on behalf of a user that could take a minute or so to complete. The results of the API lookups were cached and so once it was done the site would be very quick, unfortunately the initial API lookup slowed down the page load quite considerably so this created a problem.
Rather than just doing the API loading in the page load process and making the user sit through it I created a batch process to load the API results in a more manageable manner. This created another problem as although the batch runner in Drupal is really good, it is perhaps a little too much just to show to users and expect them to understand what is going on. This led me to think if I could run a batch process via an AJAX callback from the page they were trying to load.