Searching for free and solo board games through Board Game Geek entries, I found a game called Pocket Civ. Game is free and can be downloaded here.
Pocket Civ can be played in two versions. Light version requires only peace of paper, pen and set of event cards. This version you can play on a road, or wherever you are.
The full version is more suitable for home play, it offers more of the boardgame feel, and if you have proper counters at home, you can even make it 3D like I did.
Basically, this is worker allocation game, remotely based upon Sid Meier's Civilization.
Game is played in eras, where first few eras can be easily survived but later things get tougher and tougher.
AI is great, maybe the best thing in this game. Not only it can give you serious challenge, but the complete AI mechanism is located on a set of no more then 16 event cards! Something that every solo enthusiast should definitely look at and admire.
Another nice solution is the way the resources are taken into consideration. Simply, provinces that have mountains in it are considered to have the use of stone, etc.
The main resource in the game are tribes. Almost everything you need to build is payed by sacrificing certain amounts of tribes. In this game people are the greatest fortune. There is also a gold, but it is hard to acquire, and it is reserved as resource only for the greatest civilization achievements.
Anyway, this is a great game, something you should definitely try if you love solo play. Furthermore, it is free, so what are you waiting for? Go download it!