Something I really enjoy in games is the chance that, under perfect circumstances and/or with a perfect roll, the underdog model or player character or what have you can overcome impossible odds and make the shot, 1-hit-kill the enormous dragon, dodge what should have been a point-blank shot, etc. I also like it when the trope is flipped on it’s head, where there’s a chance to fail so spectacularly that everything is ruined utterly and completely, if you roll/plan badly enough.
A good example of this is exploding dice mechanics, and for this example I’ll use Mantic’s Deadzone. Deadzone uses d8s, and on a roll of 8, you keep the 8 and roll another die. This means with an absurdly good string of luck, one can roll a huge number of successes, enabling a model that might normally never have a chance in hell against a target have a remote chance of actually damaging it or taking it down completely.
Warhammer Fantasy Roleplay Second Edition (WHFRP) and Dark Heresy have a similar thing in that if you roll a 10 for the damage dice (All damage uses a d10, if I recall right), you roll to hit again, and if successful, roll the d10 and add that damage. At that point the d10 can explode, enabling a potentially lucky player to one-shot an otherwise incredibly durable and potent foe.
However, the “exploding” doesn’t need to specifically be “Rolling the maximum on the die means you keep it and roll another die.” I instead see it as any mechanic that allows, if you cross a certain threshold (Typically achieve the maximum or minimum result possible), to increase/decrease the effects, and allows this threshold to be crossed in another or multiple subsequent rolls.
An example of this is the rules for Chaos Manifestations in WHFRP when spellcasting. If a player rolls multiple 1s on their d10s for casting (Again, going off of my memory of the game here), depending on the number of 1s achieved a player gets a Minor, Major, or catastrophic (I forget the term used for the 3rd tier of badness) Chaos Manifestation. However, when you roll to see what occurs for a particular tier of Manifestation, a high-enough roll bumps you up to the next level of Manifestation. Minor tend to be mildly irritating things, like loud noises, curdling milk, temporary weakness or minor damage. Major include more severe damage, small demons appearing, a chance of insanity or mental scarring, and so on. The highest tier can summon greater demons into play that can and typically will slaughter the rest of the party, and the character can suffer extreme damage and possibly be killed outright.
Something I want to try eventually is an Exploding Crit system for D&D 4e. D&D 4e currently has a Critical (A roll of 20) meaning all of your damage is maximized. I’d like to offer players the chance to either take that option, or try for an Exploding Crit: They roll to hit again, and if successful, they double the damage rolled (So roll the dice for damage as normal, and double the result). The player can then either keep that, or attempt to increase the multiplier by rolling to hit again. Each additional “hit” increases the multiplier by 1x (So starting at 2x, then 3x, 4x, 5x), but if any of the attacks are missed, the attack deals the absolute minimum damage is can (So 2d6+2 would be 4 damage).
This is because 4e very much feels like a game of attrition alone during combat. Occasionally a Daily and/or Encounter is popped and it helps the fight go a little faster, but barring direct DM fiat, a single player’s round of attacks against a very tough fresh monster, like an Elite or especially a Solo, will not kill it, no matter how perfect their damage rolls are. I want to give players that ability, at the risk of them neutering their damage output.
On a final non-sequitur closing note, I’d like to recommend Ultramodern 4 for anyone who likes the 4e rules and is looking for a good modern/scifi ruleset. It uses the base 4e mechanics for modern/scifi play, and includes quite a few good solid uses of the underlying 4e mechanics, including entirely noncombat classes. I am absolutely itching to play a game using only non-combat characters in the party, and get something akin to Oceans Eleven to overcome everything with a combination of charm, threats, and fast-talking.