iOS Simulator > Menu Bar > Debug > Open System Log
Old ways:
iOS Simulator prints its logs directly to stdout, so you can see the logs mixed up with system logs.
Open the Terminal and type: tail -f /var/log/system.log
Then run the simulator.
EDIT:
This stopped working on Mavericks/Xcode 5. Now you can access the simulator logs in its own folder: ~/Library/Logs/iOS Simulator/<sim-version>/system.log
You can either use the Console.app to see this, or just do a tail (iOS 7.0.3 64 bits for example):
tail -f ~/Library/Logs/iOS\ Simulator/7.0.3-64/system.log
EDIT 2:
They are now located in ~/Library/Logs/CoreSimulator/<simulator-hash>/system.log
tail -f ~/Library/Logs/CoreSimulator/<simulator-hash>/system.log