I understand that there's a big legacy of using dice for dealing with randomness in practically all RPG's, but have anyone seen/used any other approach? Draw small scraps of paper from a hat? Stone, sax, scissors? Throw some darts and use the final score as the die-roll?
There are dozens of alternatives of course, its just dice are small and have a fairly easy to predict behavior.
Amongst the other options are to go completely free-form and have no randomizes at all, (just GM/group decision) or to use rock-paper-scissors to resolve disputes.
A deck of playing cards offers a plethora of of options. First and foremost is to use them rather like dice - draw against a difficulty rating +/- any modifiers. (Example ) A few RPGs work in actual game mechanics to this. reinforces its gambling and crime theme by playing modified black-jack. The harder the task, the more cards you're forced to draw, and thus the more likely you'll go over 21. The sadly no longer available game "Sacred Steel" used a binary card set - draw X cards, and see if the number of checks was greater than the crosses. This later version lets you add or remove cards to alter the probability for good or ill.
Then there are other physical systems such as numbering pages in a book, and rapidly flipping to one to see the result. Or having a small chart of numbers and dropping an object from a certain height to see where it falls. (these ideas are more prevalent in game books that RPGs though) I've read a few war games where artillery strikes are resolved by throwing cotton balls onto the table from a few feet away, and the original "Little Wars" by HG wells used a toy cannon for knocking down the opposing models.
Coin flips could be used in a couple of ways - everything could have a 50/50 chance baring re-trys granted by having an applicable skill or you could have X number of flips and need Y number of heads results. (Similar to the binary card draws mentioned above.) Drawing chits from a cup while not common, is a valid option of course.
If you have a specific project in mind for not using dice, I may be able to help you with the probability and choosing an alternate system.
Jenga is the mechanic in a horror game called Dread. I think this makes player dexterity the decider rather than true randomness. what happens with disabled players?
Chainsaw Aardvark: not any specific project, no, just curious! Your examples really got my mind working.
misterecho: Yes, I agree; playing Jenga is quite the horror...
I started thinking about this when I heard a friend of mine describing what I believe to be his first experience with RPG's (D&D 4e): "...and sometimes, all of a sudden, we rolled dice..." (with a dull voice). What if attribute checks required real ones? Strength-checks: lift a weight, do push-ups. Intelligence-checks: solve a puzzle, answer a question. Wisdom-checks: answer a lore-related question, explain something in-game related. And so on.
One really clever use of poker cards is in one of my favorite RPGs, Aces & Eights. When in a shootout, poker cards play very heavily on where you're going to hit. The mechanic is called the Shot Clock, a transparent sheet with a huge circular grid on it. You overlay this on an image of a cowboy (representing how your target appears to you) with the crosshairs aimed where you want like the kidney or the knee or his gun. You then roll a traditional d20 and add modifiers, this represents how accurate you were to your desired target. Unless you rolled a 25 or higher, your shot will deviate from the bullseye, and WHERE it lands depends on how much lower than 25 you rolled, and the draw of a poker card which determines a grid coordinate.
Sometimes your intention will be to shot somone in the leg to slow them down, only to hit them in the heart!