The truth of it, which may be obscured by shrill rants about 'arbitrary GMs!' and 'thousand-page rule books!' is that roleplaying games typically involve both rules and rulings, and the more interesting questions are, who gets to make rulings? and, what should the rules cover and what should be left to rulings? With respect to the first, most traditional roleplaying games answer the question of WHO DECIDES? by assigning that role to a referee, though other games may spread that role among the players to one degree or another. For now I'm going to assume the former, but when I write 'referee,' understand that I know there are other ways of doing this.
How often, and in what circumstances, the referee is called upon to make a ruling may be largely determined by the answer to the second question: what do the rules attempt to address specifically, and what is left to the discretion of the referee to adjudicate as the need arises?
One of the arguments which resonates with me for hard-coding many of these potential cruxes into the rules is that players can make informed decisions around what their characters are likely, or unlikely, to be able to do. Traditional task-resolution rules may offer a replicable, dependable game-world simulation - if I roll x, I get result y, meaning I can jump so far or hide in shadows this easily or whatever.
But the range of potential character choices is as broad as the imaginations of the players at the table. In the linked big Purple thread, one of the posters talked about knowing the DC of jumping a horse onto a boat without capsizing the craft. Is it reasonable to expect the designers of a roleplaying game to anticipate that choice with a written rule, or for a referee to remember it on the fly during actual play? In my experience, corner cases like this are exactly why rulings are necessary and desirable, because actual play often becomes one corner case after another.
The best rules, then, may be those which provide guidelines for everyone around the table, rather than, say, a rule like, "Jumping a horse onto a boat without capsizing is DC 30 for a raft, DC 40 for a dinghy, DC 25 for a barge,' &c. Of course, the nature of the guidelines becomes the next point of fracture between gamers.
I don't say much about 4e D&D because I've never played it or read it; in fact the only pieces of it I've seen first hand are the table on page 42 titled, "Difficulty Class and Damage by Level," and the section on skill challenges. As luck would have it, those are two of the sections cited in another Big Purple thread which spun off the first, as examples of how 4e makes adjudication easy, particularly for inexperienced gamers. My own feeling is that page 42 may constrain as much as it inspires and the repetitive margins for success can lead to 'flat' encounters, and that skill challenges are just a hot mess, but I can definitely understand the appeal they hold for others - replicable, reliable math is nothing to sneeze at, particularly in games with lots of fiddly bits.
Flashing Blades takes a different approach. Here's the section on how skills are handled.
During the course of an adventure, characters will wish to make constant use of their skills. This is achieved normally by rolling a D20 against one of the character's attributes. A roll equal to or less than the attribute indicates that the skill was used successfully.It's clean and simple - no Disneyland, no live nude girls. Roll against the applicable attribute, or against that attribute divided by two or three, maybe get a modifier, maybe make an opposed roll. Broad guidelines, broadly applicable. The math is reasonably consistent, too, in that a player knows what his attributes are, and the referee simply needs to let the player know what the relative difficulty is - roll under the attribute? roll under half the attribute? - and any applicable modifiers, and perhaps make an opposition roll. The rules also imply, through the combat section, that skill checks may be interpreted as degrees of success.
The attribute rolled against is usually the base attribute for the skill, but this may vary depending upon the circumstances. For instance, a character with Acrobatics skill might roll against his Dexterity to put on a 'sham' brawl, but would be required to make a roll against his Wit to recognize one if he saw it. The difficulty of most rolls will vary widely, so the Gamemaster should add bonuses or subtract penalties from the needed roll as indicated by the situation. For example, a character with Stealth skill, and a Dexterity of 13 would normally need to roll 13 or less to hide effectively. If there were no shadows and little cover, he might receive a -2 penalty, making his needed roll 11 or less. Likewise, if it were late at night in a thick forest, he might get a +4 bonus, making his required roll a 17 or less. In cases of extreme difficulty, the Gamemaster might require a roll under a given attribute divided by two or three (always round up).
When two characters use their skills in opposition to each other, it becomes a resistance roll. The first character's roll modifies the second's by the difference between his roll and what he needed. Thus, if a character with Stealth and a Dexterity of 12 were running through a forest, he might be required to make a roll against Dexterity to leave a sparse trail for his pursuer. If he rolled an 8, any character tracking him would receive a -4 penalty (8 - 12 = -4). If he missed and rolled a 15, any character tracking him would get a +3 bonus (15 - 12 = 3).
Resistance rolls are used commonly with Cut Purse, Disguise, Forgery, Stealth, Tracking, and Espionage.
In some cases, skills will only modify normal rolls. For instance, if a character were standing on top of a table about to be flipped by an enemy, he might be required to make a roll against Dexterity to jump down in time. Acrobatics skill might give him a +3 bonus.
I don't know if this would satisfy 'jumping a horse onto a boat without capsizing it is DC 30' guy or 'page 42 makes anyone a competent referee' guy, but as a player it lets me have some idea of what it takes to accomplish something and as a referee it provides me with a framework on which to adjudicate the action as the players make their choices. I don't want a folio of rules which try to cover every corner case, like 'horse jump' guy, and I don't need one rule that applies to every possible corner case, like 'page 42' guy.