Far Cry 4 players have experienced several issues on launch day, and Ubisoft has acknowledged some of thus far on its official Live Updates blog.
Some PC players have experienced black-screen crashes, a minority of PS3 players have seen FC3 game data been corrupted even if they have never played Far Cry 3 on that console, and some pre-order redemption codes for the "Blood Ruby" bonus mission have not worked or haven't been received. Ubisoft is working to address and fix all of these issues.
Currently, Ubisoft suggests that you have the Day 1 Patch installed and checked, though it seems that the 1,554 comments (and rising) on the launch day blog post will pressure the development team to patch up the game as soon as possible.