The longest running solo player game I've run used BESM 3E. As with most RPGs designed for a group of PCs, there are a lot of factors to take into account with a single player (action economy, more gaps in skills, getting stuck if that one PC fails at a critical moment, etc.). But we've made it work, mostly by making her character fairly powerful on her own, giving her an NPC companion, and having many situations resolved through role-playing rather than fighting.
Trail of Cthulhu and Gumshoe have "Confidential" campaign books designed for one player and one GM, but I haven't played either version of either game. But from what I've heard on the creators' podcast, the saving grace of those solo games is that the base game system takes the approach that the PCs are highly competent at their professions, and always get the clue they need to continue to the next part of the story. Failure just means that progress comes at a higher price (expending more resources, getting injured, etc.).