The Traveller RPG character generation mini-game can be quite fun solo (if you try to think of reasons and stories to explain the ups and downs of you characters life - more fun if you set some goals like "I want my Navy character to retire as an Admiral" or "I want my wastrel Noble to be more famous than the Emperor".
The old Lone Wolf books used to be solo-play, choose your own adventure type things.
Boardgamewise, its not Mongoose, but I would recommend Arkham Horror- that can be played against the board/cards and makes for quite a fun Cthulhu experience if you try to tie it all together.
SJE