A recent forum thread at RPG.net and the revival of the Solo Wargaming Show has made me think about the Boardgames that I have for solo play. These are not all exclusively solo games by design, but some multiplayer games are easily adapted or have solo scenarios or rules included.
To start with ones that I own and are designed for solo play:
Ambush is a very good solo game that I've owned since it came out. The play method with the actions of the Germans coming from a set of numbered paragraphs in a book is similar in some ways to the choose your own adventure games like Warlock of Firetop Mountain, but less linear due to the fact that there are far more possible locations for the American squad on the map and it is a squad rather than an individual.
I've not played this for a good while, but I do intend to some time this year and I'll post a review when I do. I remember that it does play very well with a roleplaying element from the US squad being the same named individuals (allowing for casualties) through the scenarios and they are able to improve with experience.
The programmed elements are a lot less predictable than it might be thought, though I would not want to play the same scenario two or three times in a short timescale as it would tend to make things a bit 'samey'. I remember that there is one trap in the numbered paragraphs from having read through idly after playing through all the scenarios back in the 1980s and that is the one with the Dragon in it. This does not actually turn up in play though.
This is recommended to any solo gamer out there who wants a squad level WWII infantry game, I think it is pretty readily available via ebay and second hand games stores.