Gus L, who runs the ongoing HMS Apollyon campaign online and the Dungeon of Signs blog, has posted a detailed long post about his modified skill system being used in the campaign, which are based from on the system used in Lamentations of the Flame Princess [AL]. As Gus explains it, these skills are able to be used by multiple classes, as well as take the place of some spells, and can be used in a number of circumstances that adventurers may find themselves in. The chief idea behind skills in old school games, as Gus points out, is that the skills should focus on those circumstances where some sort of mechanical element occurs.
In games with class-based systems that strictly limit what classes can do certain things, having skills be able to be performed by all characters is a good thing. For many years during my initial gaming, I disliked class-based gaming because it heavily restricted what characters could or could not do by having certain things baked into the rules, and so my choice of fantasy game for many years was either Rolemaster or Runequest [AL] rather than Dungeons & Dragons [AL].