A parent of a Doctor Who fan wanted a Doctor Who story game with ultra-simple rules. If you have recommendations, please post them on this thread. For my part, I took a quick pass at a system. Hopefully it kind of fits the bill.
The game begins with ten stones on the table. This represents the problem on the new world you're visiting. When you land on the world, you don't know what the problems are.
How You Solve the Problem
Each turn, the Doctor can do one of three things to help: Talk, Search or Make. When you Talk, this means you're making friends with someone or trying to scare someone. When you Search, this means you're finding clues about the problem. When you Make, you're creating a new gadget or helping to repair an existing one. Describe your character doing one of these things to solve the problem. After describing what the Doctor does to help, roll d6.
If the result is 1-2, add that many stones to the table. This means something you did made the situation worse or simply that you're running out of time.
If the result is 3-6, remove that many stones. This means that whatever you did is starting to help. That's no guarantee it'll work a second time, though!
Saving the World
When there are no more stones on the table, you saved the world!
When there are twenty stones on the table, the Doctor is forced to regenerate. The Doctor's appearance and personality can shift radically after regeneration. This also means the Doctor approaches old problems with new insights. Reduce the number of stones back down to ten.
The Doctor gets +1 to Talking rolls when using Psychic Paper.
The Doctor gets +1 to Searching rolls when using the TARDIS.
The Doctor gets +1 to Making rolls when using the sonic screwdriver.