I started playing RPGs solo as a way to teach myself systems and procedures on the off chance that I could find other people to play with. After dalliances with Knave 2e (great), Basic Fantasy RPG (less great), and Starforged (incredible), I started in on SoloDark.
Seeing that most of the ShadowDark core book is random tables, it fits well with solo game play. It has a monster creator, dungeon namer, quest generator, a “something happens” table, and random encounters for a wide variety of environments. One of the really neat things is that. It is missing a few things, namely a spark table and a yes/no oracle.
Fortunately the SoloDark rules take care of that with two d100 noun-verb tables, and a yes/no oracle with a really simple “likely-less likely” mechanic that I kicked myself for not coming up with.
It’s a really complete stand alone system and works great for solo play with no additional resources.
But I’m extra. In addition to Lodestar, I used Knave 2e and the Hazard System to help keep the story moving.
Adventures were procedurally generated, which is my current preferred method of playing. I use my Oracles a lot in solo play, but I've started to use them in group play as well.