One of the questions I've been wrestling with is a skill system, and whether or not to include one in System X. And if so, what kind of system it should be.
In the original OD&D (that's the Dungeons and Dragons before 2nd edition), there was no skill system. Certain classes had skill-like abilities, notably the Thief. (Actually, that's the only class that comes to mind.) They had a percentage chance to pick locks, disarm traps, and so on. If something resembling a skill cropped up in a game, such as successfully swimming a raging river or appraising a gem, my referee usually called for a simple attribute check. We seemed to get along fine. The game didn't seem to suffer without a skill system.
Then along came Traveller, and it had a skill system, since it didn't really have professional classes. Call of Cthulhu was the next system to include skills, since those also defined a character's profession. Ever since then, a method for defining skills and resolving their use has become integral to game design. I can't see designing a game without one. Characters would seem somehow diminished without skills.
There exist currently two kinds of skill system:
1) Roll dice and try to attain a result lower than the character's skill level. Thus, if your character has a 40 percent chance to swim a river, the player must roll under 40 percent. Or in a d20 based system, you have to roll under your skill level 12 on a 20-sided die. As you gain in skill levels, your chances to roll under that "target number" increases. This, however, violates the "higher is better" meme that runs through contemporary gaming.
2) Target Number. Your character has a skill level, and the referee sets what is known as a "target number" you must beat, typically by adding your skill level as a modifier to a dice roll. The harder the action being attempted, the higher the target number. While this adheres to the "higher is better" ideal, it also places a lot of responsibility on the referee (since he's defining the target number). Some games have tried to ameliorate some stress here by giving lists of sample target numbers.
Something I've been toying with is the "opposed test." I stumbled upon this idea when designing the Coda System for Decipher, and I was quite taken with it. Most skill tests players will get involved with are, in fact, opposed tests. That is to say, one player is pitting his dice result against the dice result of another player. One player tries to hit the orc with his sword, while the orc (played by the referee) tries to avoid this; one rolls "to hit", the other "to not get hit". That's the simplest, most common example.
But what if a character searches a room for a hidden clue? Why not roll the hiding character's skill test for hiding things? The latter becomes the "target number" for the former. Dave and Buster chase each other down the street in cars, both trying to run the other off the road. Dave rolls to ram Buster, while Buster (played by the referee) rolls to avoid this. Both make driving rolls, with the higher result the winner. You could make the case that almost every skill test opposes another character's skill test, either immediately (combat) or through time (as with the hidden clue).
The rest of the time, you could use the standard target number system. There's nothing opposing the character except circumstances, fate, or nature. The characters need to appraise the value of the diamond they've just stolen, so that's a simple target number test. They need to climb a sheer cliff, roll versus a target number.
To me, this doesn't seem like anything different from the typical skill test system used by the majority of games today. Except for the emphasis on opposition; the referee doesn't set target numbers for the majority of tests. Players roll off against each other.