Server Down
Occasionally, the "Uncharted" servers are taken down for maintenance or to implement preparations for future patches. Most of the time, a maintenance message is displayed when attempting to connect when the server is down, though it's not uncommon for the "Connecting..." screen to freeze while the maintenance is taking place.
Router Settings
Depending on the complexity of your network and whether you're using a wired or wireless connection, your router may be preventing you from connecting to the "Uncharted" servers, even though you may be able to connect to the PlayStation Network. Verify that your router settings match up with what the PlayStation 3 is detecting from the Network Settings menu on the PS3.
Data Sync
If it's your first time connecting to the "Uncharted" servers, the PS3 must perform a data sync before you'll have access to the multiplayer lobby. The synchronization process may take some time depending on your Internet connection speed and server load. The data sync is a one time process and doesn't affect your single player data.
Incompatible Firmware
If you're using a custom PS3 firmware, it could cause connections issues when trying to connect to the "Uncharted" multiplayer service. If none of the aforementioned solutions work, you may be required to revert to an official PS3 firmware before being able to access the "Uncharted" multiplayer.