Most of the unlockable characters are gotten by earning a certain amount of experience points. Each day survived earns you 20 experience and the total amount of experience you have is cumulative over all of your games played. Wes and Maxwell are the exceptions to this, and they can only be unlocked through playing Adventure Mode.

Character	How to unlock
Maxwell	Complete Adventure Mode.
Wendy	Survive a total of 32 days (640 exp)
Wes	Find a rescue Wes in Adventure Mode. Whether he spawns or not is random.
Wickerbottom	Survive a total of 64 days (1280 exp)
Willow	Survive a total of 8 days (160 exp)
Wolfgang	Survive a total of 16 days (320 exp)
Woodie	Survive a total of 80 days (1600 exp)
WX-78	Survive a total of 48 days (960 exp)