Dice Mechanics

Linear Distribution (Single dice, or unrelated sequential dice)

D20/D30/D%/Polyhedral 

1. Polyhedra: Uses d4-d12, and sometimes d20, more rarely d14, d16, d18. 
2. True20 : D20 used for all rolls Ex: True 20
3. D20 & polyhedra: D20 used to check successes, other dice use for success magnitude (most D20)
4. Roll+X: Any of the above, but add a fixed number to the roll.
5. Criticals: As above, but 1 is always a failure, a 20 is always a success. Ex: DnD 4e
6. D100: Use two D10 to determine a percent score. Ex: GURPS

NON-LINEAR (Dice-sum, dice-pool, and 'fat tails')

DICE-SUM (Normal Distribution)

1. xDx: Roll between 2-5 dice, sum the result. D6 and D10 are by far the most common.
2. xDx+x: As above, but add a fixed number to the roll. Ex: Green Ronin AGE system.
3. xDx+Dx: As above, but add a non-standard die to the roll. Ex: Monsters & Magic uses Roll+dX, with the base roll being 3d6. 
4. xDx&Dx: Sum a pool of dice to determine success or failure, and then roll a second die to determine the degree of success or failure. Ex: Chivalry and Sorcery. 
5. FUDGE: Roll 4d6, sum after using the conversion that 1-2=-1, 3-4=0, 5-6 = 1. ( FUDGE dice are almost necessary)
6. Attributes: Roll 2d6 or 3d6: The median value counts as a zero. The next great value (or pair of greater values for 3d6) counts as a +1, so that that the range is -5 to +5.
7. Flux: Two different colour dice (D6) are rolled, one positive, one negative - the lowest value is taken or if the same =0. Yields results -5 to +5. Ex: Traveler 5
8. Opposed Rolls: Rather than a fixed DC, defense is also rolled, and subtracted from the attack roll to determine success. Ties may be treated as partial successes. Ex: Mayhem

DICEPOOL (Binomial or Negative Binomial Distribution)

1. Success: Roll a number of dice; a die that rolls a certain number or greater counts as a success. D6 and D10 are most common. Typically between half and one third of numbers count as a success. 
1. Count: As per 'Success', but the count of successes matter.
2. Exploding dice: A dice-sum system where the highest value of die triggers the addition of another die of the same type: ie, rolling a 6 on a d6 means another d6 is rolled. 
3. Failure: Every natural 1 has negative consequences.
4. Mixed Pool: A dicepool that contains a variety of different dice.
2. Keep: Roll a number of dice, keep the one with the highest value, treating that as the outcome of the roll.
1. Keep Two: As per Keep, but keep the two highest dice and sum them. 
2. Keep+Count: Take the highest value from a pool, add +1 for other 'success'
3. Keep+Match: Take the highest value from a pool, add +1 for every dice also equal to that value. Ex: Heavy Gear, Pod 9.
4. Wild Dice: Roll two polyhedral dice, one default, one defined by a skill or attribute, and take the higher. Ex: Savage Worlds. 
1. Advantage: Roll 2d20, take the better or the worse. Ex: DnD 5e

ERRATIC DISTRIBUTIONS

1. STEP/RANK: At each rank, the dice rolled changes so as to represent an improvement in the median roll. Ie 1d10->1d12->2d6->d8+d6. Ex: Earthdawn.
2. One Roll Engine (ORE): A dicepool system where values in the pool are grouped into sets; the value is called the 'height', the number in the set is called the 'width'.

"ORE (One Roll Engine) you roll a pool of 2-9 D10 and count matches. The number of matching dice is the width of the roll, and the number of the match is the height. A hard die is always 10, and a wiggle die have any number decided after the dice are rolled. For damage rolls, the width determines amount of damage, and the height determines hit locations. For most generic actions the width is the speed of the action and the height the quality. It is possible to get multiple matches in a single roll, which is how doing multiple actions in one round is handled. " - Jesper Anderson

TN & DC Alternates (Target Numbers, Difficulty Classes)

1. Roll Under: Roll under a fixed attribute, so that low roles are good, bonuses as negative numbers. EX: Advanced Dungeons and Dragons ('Whitebox', 2E) 
2. DC+X: Roll over a fixed attribute, so bonuses are positive numbers. Ex: DnD 3E, 3.5,4, 
3. Margin Triggers: A linear system where beating a DC by a certain number generates an additional effect, often a damage 'critical'. (Mayhem)
4. Risks/Raises: Before rolling, players may reduce their dice pool to obtain additional effects on a successful outcome.
5. TC based on the sum of several attributes

OUTCOMES
With a linear distribution, outcomes are fully random within a certain range; above that range, failure is inevitable. Below that range, success is inevitable. Dice-sum systems generate consistent bell-curves of which the median, minima and maxima are known. Estimating chances of success on a role is more difficult. Reference tables are necessary.  The effect of a +1 bonus is non-linear, but tends to 'auto-balance', as the value of a +1 is greater to the underdog. Dicepool systems where success is binary follow a binomial distribution. Systems that count successes follow a negative binomial distribution. Failure is always possible, although statistically unlikely. Including additional negative effects for 'natural 1;s' can be used to make failure more painful, or more common. Reference tables to estimate success are necessary. With large pools of dice, failures are rare, and large pools may (rarely) generate an awesomely large count of successes.

NOTABLE SYSTEMS

 Travis Casey

The horror RPG "Don't Look Back" uses this: Base roll is 3d6. If you have a bonus, you roll additional d6 equal to the bonus value to your roll, but only take the best three. If you have a penalty, roll additional d6 equal to the penalty value and take the worst three. Bonuses and penalties add together - e.g., a +2 bonus and -3 penalty become a -1 penalty.  Action value is the name for the degree of success. If i succeed by 5 i have a +5 action value. If i fail by 3 i have a -3 action value. In an opposed test, those with the highest positive action value win the contest.

Also note that the "d20/polyhedra" system you have there is used with many other games that don't use a d20 as the basic roll. A lot of old systems use a separate "damage die" in combat. A similar concept is also seen in 3rd edition Chivalry & Sorcery: you roll 2d10 to determine success/failure, and an additional d10 of a different color, which determines degree of success/failure. Green Ronin's "AGE" system uses 3d6, one of which is a different color. All three are added together, along with an attribute bonus, but one of the three is special and generates "stunt points" that can be used if you succeed.