In the home screen of Dumb Ways to Die, there is a train station where all unlocked beans are shown. Older versions of the game only required to accumulate a few points to unlock all characters, but nowadays, one has to collect thousands and thousands of points to access new characters.
To unlock all characters in Dumb Ways to Die, you can complete mini-game challenges, achieve high scores, watch promotional videos, earn in-game currency, and participate in special events.
Here are all the characters obtainable through collecting points in Dumb Ways to Die:
In the bottom left corner of the home screen, you can see how many points are needed to unlock the next character. There are other characters besides these, but some are given out during events, so you may not be able to get them later, and a few are also obtainable by completing daily challenges.