Most contemporary RPG systems have a list of skills characters can possess. These can range from simple checklists of a few general areas, to vast indexes of possible fields.
To illustrate, let's look at what skill sets might look like for the two most common RPG skill fields, combat and social interaction. Games with broad skills might have a single skill called "Melee" or "Influence" that cover the entire category with a single statistic. Moderately specific games might have a number of different skills, like "Diplomacy," "Intimidate," "Sword," or "Polearm." Games with truly narrow lists might have dozens of categories of each - "Public Speaking," "Interrogation," "Rapier," and "Guisarme-Voulge."
Some games use a mix of different levels, indicating the system's intended focus. A hack-and-slash dungeon crawler-might have 20 combat skills and one social skill, whereas a highbrow narrative system might have the reverse.
Other systems mix various levels by allowing or requiring specializations within broader categories. Various incarnations of D&D and WoD have allowed players to advance general combat skill, but include some abilities or rules grant special bonuses for using their weapon of choice. Some variants of the FUDGE system ignore the distinction entirely, allowing players to make up skills/traits as narrow or specific as their GM will allow.
However, I'm more interested in the values and advantages of the different categories.
Broad skill categories seem to be on the upswing - most indy RP systems these days use very limited skill lists, providing a basic mechanical outline and assuming the players can just roleplay the specifics as they like. Dungeons and Dragons cut its skill list in half for 4th Edition, going from 36 core skills to 18. Broak skill lists are probably the most mechanically elegant, because they streamline character creation and gameplay at little cost of mechanical relevance.
The advantage to moderately specific skills is not one of mechanics, but one of characterization. While some argue that roleplaying should be the responsibility of player rather than the rules, I've always been a big believer in encouraging characterization through the system itself. I think it is important to provide rules that allow a character sheet to show the difference between the Green Arrow's skill at archery, Batman's skill with batarangs, and the Punisher's skill with guns. (Yes, that's a geeky example. Yes, I'm mixing Marvel and DC characters.)
Narrow skill list have always been pretty rare, except as optional specializations. GURPS is the only system I'm familiar with that uses truly specific skills as the core list. The GURPS skill list is somewhat absurd, containing over 350 entries and a wide variety of everyday skills including Accounting, Economics, Administration and Finance. Even if these are distinct skill sets in real life, I can't imagine that level of specificity serving much purpose as a roleplaying mechanic.
I'm looking into some ways of trying to find a balance between mechanical elegance and creative freedom. I think the best option may be a variant of the systems that involve general proficiencies with optional specializations.