As long as you have logged into the plug-ins you would be able to export all your passwords, even with LastPass completely gone - this is possible because a locally-cached copy of your data is stored by default when you use the LastPass plugin or LastPass mobile apps. To use any of the exporting options you can go to your LastPass Icon > Tools > Export To.

LastPass Pocket is also offered for backup access on your USB/portable drive.

You can also re-import your passwords back into the Internet Explorer and Firefox password managers.

That being said, we're spread across 2 data centers, 2 countries, and have a team of people who can each run the service individually.  We're stable, profitable and we have no plans of going anywhere -- we depend on LastPass too!