One of the issues I've come across in various games is the disuse of average skills. Players generally prefer to use their best skills. The reason is fairly obvious, players want to succeed at what they are doing and so they attempt to solve problems using the skills they are good at.
This habit can lead to a bunch of unused or rarely used skills. While this might lead to a good simulation of a character's actual abilities I feel that it is generally unnecessary to have all those extra skills.
Different games do different things to deal with this. Some games use multiple different solutions. I am going to use the word skill to represent anything that could provide a mechanical bonus to a player.
Every Skills Is Useful
This is probably the most common solution. Every skill is useful in different situations and it is the GM's job to make sure that they get used. Skills usually have a fixed breadth of what they can accomplish so that the GM can make every skill useful in different ways.
The problem is that in groups of players the character with the highest skill is always making that type of roll. It also doesn't solve the problem of the players always trying to solve a problem in ways they are good at.
Examples
Almost everything in D&D
Skills in Spirit of the Century
Resource based skills
This method has some sort of balance system for the skill. Maybe you only have so many dice that you can use for the skill during a session, maybe you have to spend points to gain a benefit.
There is something appealing about this sort of skill system. Since a player can still usually get one or two good rolls out of a weaker skill then they will want to try it occasionally. It could also be that using one skill is equivalent to using another because they all come from the same pool and then the player will just go with whichever seems most appropriate.
Examples
Everything in Trail of Cthulhu
Aspects in Spirit of the Century
Traits and Fan Mail in Primetime Adventures
Organic Growth
If an organic character growth advancement system involves increasing skills that you use then if falls into this category. That rewards the player for using their weaker skills because that is the way that they get better. Since it is harder to improve higher skills it can be more beneficial to use the lower skills because it is easier to improve them.
Examples
Advancement System in Burning Wheel