Pain which led to this will be most understood by people who require visa for a lot of their trips.
Currently all embassies have slightly different application forms and either online or offline they are most of the times very painful to fill-in. US visa requires IE and Windows, and you need to save the backup file almost every 5 questions (out of around 100 I think). All these steps for all embassy web-sites I used contain usually highly unusable form elements choice. :)
Imagine you fill in application form only once online with all questions asked in embassies of countries you are planning to travel to. Imagine this form is very usable and has nice features as auto-saving etc.
Then ideally embassies would support this format and just get the data they need, they could do it, for example, using OAuth used by Facebook, Twitter etc. Of course, it's much faster not to wait for that :), so there there should be an API for developers to create conversion tools to formats of different embassies. Ideally of course this tool would be open-source.
This idea could be pushed much further outside of this scope, imagine you are in control of all of your data and you have online passport in the cloud. You should be able to have an easy control of what web-sites/applications should be able to get what information. Separate web-applications are already implementing that approach - Facebook, Google's Android Market, Apple's App Store, but this should be much more unified in my opinion.
Image courtesy of: Lady the Tramp