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Let's start with a few definitions:
- Permissive skill systems - assume that characters are capable and allow characters to attempt any task
- Restrictive skill systems - assume that some or all skills are impossible to attempt without training
- Broad skills - skills that pertain to a widely defined abilities such a all technology, combat, all vehicle types, and the like
- Narrow skills - skills that pertain to specifically defined abilities, often task oriented with skills to cover individual aspects of a broad category such as individual sciences, or breaking ranged combat skills out into pistols, rifles, bows, etc.
- Open Skills - a subset of broad skills, using a user defined skills rather than an inclusive list
Different systems for skills will lend a different flavor to game play. Broad and permissive systems lend a more heroic feel where characters are very capable and able to overcome any challenge. Narrow and restrictive systems lead to characters with tight focus who can quickly find themselves out of their depth.
Regardless of the skill system of your chosen game selection of skills by the players should help inform the GM of the kinds of stories to tell. A player who has skills pertaining to espionage will want to use said skills. Often is this little trouble, especially if the scope of the game is laid out for the players during character creation, but if a player chooses skills that may not intersect with the scope of the GM's intent it may signal a potential disconnect between the player and the GM. Such situations are an opportunity to head off player dissatisfaction before it occurs by discussing with the player and recalibrating the game or the players concept accordingly.
Likewise open skill systems afford the opportunity to approach skills differently. Rather than using task oriented skills an open system can use professions or trade. Having training as a "spy" yields a broad skill base in tasks like cryptography, stealth, surveillance, and the like. This approach is used in 13th Age, allowing characters to have had prior careers before becoming adventurers, and works well to help generate depth to character background while putting their skills and training into a useful context.
Regardless of the skill systems you use, consider how your skills speak to your character, how they inform your character's abilities and what you want to be able to do in game. Even if you don't use careers or professions as skills consider what your character did in the past and what kinds of training this would result in that would filter into the skill system of your game. Skill may not have the play impact of combat abilities or spells, but they speak as loudly or more so as those traits in defining a character's past.