In running and playing various role-playing games over the years, I've encountered some of the same issues repeatedly. I don't mean to imply that these problems are entirely with the games themselves - Perhaps these are just issues that occur based on my style of running and playing.
1) Players like rolling dice, assuming that it's for combat or some other exciting phase of the adventure. However, players don't much care for rolling dice to see if they can run to the other side of an empty room without falling down, or to see if they know how to turn on a computer in a modern day setting.
Solution: Players roll for any action where there's a reasonable chance that they may not be successful. They roll a group of dice based on how much ability they have. In some cases, just having a certain level of skill allows an action to succeed automatically.
2) If players spend "points" or "picks" on a skill/ability/perk, then they want it to have some effect in game. Likewise, if characters gain a "level", then they want to have everything improve, not just certain things.
In d20, a character might have a base attack of +0 at first level, +1 at second level AND third level, not improving any further until fourth level. Or, the character may have a STR of 13 (+1), but wonder why he would bother to spend more points when a 12 is also +1. One might argue that the character with a 13 is closer to having a larger bonus when they get a "+1 to STR" magic item, or they are 1 point closer to getting +2 when they finally get to add 1 to a stat. But, having a future opportunity to get an additional +1 doesn't seem to be worth it if you're spending points that could be used on other abilities right now.
Solution: Regardless of the dice mechanics (d100 -vs- d20 -vs- Xd6), there should be a measureable difference between the values, whether it's a 12 and a 13, or a 70 and a 71.
3) Lore or Knowledge skills suck because they are either generally unhelpful or players select areas of knowledge that are not applicable to any adventures they are involved in. And, GMs should not be forced to add a situation into an adventure that requires a specific skill chosen by the player.
Solution: Unless a player purposely decides that they should have a specific area of knowledge, the individual lore skills are selected when the player decides that they are needed. A player does not normally describe a character down to the exact details of every event that has ever occurred in their lives, so it would not be against a story or plot to have a character just so happen to know certain things.
4) Critical hits suck because, although they sell themselves as making combat exciting, they end up killing characters.
Solution: Give players the option "disable" critical effects on a character by character basis. Some players will want to have intense, bloody combat, while others don't want (through no fault of their own) to have their character cut down, ending their adventuring careers. The characters that have criticals "disabled" will also be unable to deal critical effects, allowing characters of either type to be within the same group.
5) Critical failures (fumbles) suck because no one thinks that an experienced warrior should ever drop his weapon and trip over it. Mages should not stun themselves into next week when casting a simple spell that they normally cast over and over. Expert snipers should not shoot themselves in the foot when attempting to shoot an enemy at long range.
Solution: Don't use them.
6) Almost no one creates a specific character and thinks "ok, my guy is terrible at everything, but in a few adventures he will be generally competent." But, no sane GM thinks "I think that all characters should start with mastery in each of their primary fields of ability."
Solution: Starting off, characters should be "good" with their primary abilities. "Good" could also be described as "Unmistakenly above average."
7) Although adventures can go in many different directions, combat skills are almost always the deciding factor. Characters who specialize in non-combat spells, knowledge skills, social skills, and the like are at a recognizable disadvantage. But, an RPG without these other skills seems incomplete.
Solution: Create groups of (vaguely) related skills and make them ALL have some purpose. Give these skills a reason to exist on a player's character sheet.
8) In general, complexity sucks.
Players and (to a lesser extent) GMs like having a wide arry of options, especially when making characters and personalizing them. Having only a few heavily restricted, specialized character types with no varying skills or abilities isn't fun. And, combat that boils down to "I attack, they attack, I attack, they attack, I attack..." is boring.
But - Having the GMs rehearsed, atmospheric narration interrupted by skill rolls and rulebook cross-referencing just plain sucks. Having an epic final battle with the primary antagonist turns tedious when each player's turn takes 15+ minutes, looking up rules and rolling several times just to complete a single movement action.
Solution: Find the middle ground.
In this case, there are a wide variey of options, but the actual effects also widely vary. Each option has the potential to make a difference, but is treated as a single additional die.