Patch 1.06 is the latest version; use the manual download link if the Uplay client does not install it automatically.
%USERPROFILE%\Documents\Assassin's Creed III\
The save file may be corrupted. Deleting the save file (after backing it up) and disabling automatic cloud save sync in Uplay may fix the crashing.
If you experience low FPS while running a crossfire setup, try disabling crossfire (running the game with only one card). This can be done under the "Performance" section of the AMD Catalyst Control Center, under the CrossfireX tab.
3D Settings -> Manage 3D Settings
Multi-Frame Sampled AA (MFAA)
Windows may be out-of-date. Install all Recommended updates via Windows Update.
unlock voltage control and monitoring
Verify Integrity of Game Cache
The use of Comodo Firewall may cause computer crashes. To solve this:
The game will refuse to run when installed on a drive which is managed by a Storage Space on Windows 8 and later.
Attempting to play multiplayer may result in a "kicked from server by PunkBuster" error.