Unable to open any save games after patch

Solution 1:

Some players not being able to load saves is a known bug in Title Update 9 (TU9):

Xbox Live Silver Members sometimes may not be able to load old saves.

TU9 is riddled with show-stopping bugs, and TU10 is apparently under feverish development to fix the fiasco TU9 is causing.

The only free, permanent solution is to wait for the update. The more immediate solution is to pay for a Gold membership. A temporary work-around is to disconnect your Xbox's Internet (either unplugging the cable, or turning off your wireless router) before starting Minecraft and loading your world, then reconnecting/turning it back on after your world is loaded.