Obviously ordinary standard six-sided dice can be substituted for the new design by simply giving a spotted number a corresponding symbol, letter or word from the face of the new die.

Sometimes dice are marked with the numerals 1, 2, 3, 4, 5, 6 instead of spots.  This is a Role Playing Game (RPG) convention and, of course, they can be used in exactly the same way as the standard ordinary spotted dice.  Similarly, but less common, some dice are marked with Roman numerals - I, II, III, IV, V, VI.  The six numbers on a standard dice can also be represented by words spelling out the values: "one", "two", "three", "four", "five", "six".

You may come across dice that are not marked with the usual round spots but use a small symbol as a replacement for the common and usual circular dot.  They are marked with the symbol conventionally so each face has one up to six symbols arranged like an ordinary standard die's spots.  Symbols used include - stars, hearts, dollar signs, champagne glasses, pumpkins, shamrocks, Christmas trees, horseshoes.

Some common specially marked cubic dice include...

Poker Dice are the most common pictured dice available and have playing cards printed on them (A, K, Q, J, 10, 9).  No particular suits are assigned to the King, Queen and Jack while the 10 is usually a diamond or sometimes a heart and the 9 may be either a spade or club.  The Ace is usually a spade but very occasionally a club.  Poker dice come in sets of five. See Poke Dice Games for a list of games played with a set.   

Spanish Poker dice are much the same as standard Poker dice but they have a large red spot (instead of a black Ace), red letter K (instead of a King picture), black letter Q (instead of a Queen picture), black letter J (instead of a Jack picture), 8 red spots (instead of ten hearts or diamonds), and 7 black spots (instead of nine clubs or spades).  They come in sets of five and are played in exactly the same way as standard ordinary Poker dice except that runs of five consecutive values aren't possible.

Crown and Anchor dice have a club, diamond, spade, heart, crown and anchor printed on them   It is thought they originated in Australia.  They come in sets of three and are really only a gimmick on the game of Chuck-A-Luck.  In Belgium and Flemish France, where they call the game Ancre, Pique et Soleil, they use a Sun symbol instead of a crown while in Nepal they use a flag symbol and call it Langurburjar simply meaning dice.  It's believed the Nepalese adopted the game from British, Dutch, Belgian and French sailors.  

There are other dice with the playing card suit symbols but without the crown and anchor.  There are also dice with a heart, spade and two clubs and two diamonds.  Anyone know how they are used?

Bar or Slots dice are marked with slot machine symbols - cherries, lemon, Barr, Jackpot, melon, etc.  Usually found in sets of three these are used for gambling with payoffs for triples and cherries etc.

Pig and other games are sometimes played with Death Dice that have a skull instead of a 1-spot.

Hearts dice come in sets of six and have letters (H, E, A, R, T and S) instead of spots.  They are an old gimmick on the game of Sequences.

Beetle dice have letters to represent a beetle's body parts: B-ody, H-ead, E-ye, L-eg, A-nttenae and T-ail.  A single die, or sometimes a pair, is used for this game.

There have been many commercially marketed dice games that use dice with letters of the alphabet (A - Z) printed on their faces.  These games often require the player to make words from the letters thrown in a Scrabble or anagram type game.  Some games that use letter dice include Boggle, Word Yahtzee, Scrabble Dice, and Spill & Spell.

Similarly dice with numerals and/or mathematical operators (+, -, /, x) and/or fractions are used in commercial and educational math games.

Dice marked 2, 4, 8, 16, 32, 64 are doubling cubes used for gambling in the board game Backgammon.  Players double their bets during a game and turn the cube face up accordingly to show this.

Put and Take dice come in pairs and are a variation on the spinner game.  They have letters and numbers - P and T three times on one and 1, 2, 3, A on the other.

Words on dice are another commercially used method of marking dice.  Dice are marked with different instructional words that players must obey or have categories that are selected by rolling a die.  Many Role Playing Games use dice like this. 

There are dice marked with different toppings (onions, extra cheese, pepperoni) that can be used for deciding your pizza when ordering.  Similarly there are dice marked with different activities like TV, Disco, Bar, Read, etc.  Erotic dice have intimate and sensuous instructions and areas of the body printed on them (for example kiss, touch, massage and neck, back, leg).

A number of sports have been interpreted as dice games by printing the sport's common terms or actions on cubes.  Sports like snooker, football, cricket, golf, bowls and tennis have all been given less strenuous dice rolling alternative treatments.  Examples are - In Off The Black, Goal, Not Out, Caught, On the Green, Return, Touch Down, etc. 

Dice with images of different drinks can be used for deciding what to have in a bar, and there are Karma Sutra dice marked with illustrations from the book.

Some dice simply have different colours marked on each face for young children to make a selection.

Fudge dice were developed for the Fudge game but can be incorporated in many other games if you want to.  A Fudge die is marked twice with '+', '-' and two blank sides.  A number of Fudge dice are used and any + signs mean add 1, a minus sign means subtract 1 and a blank side represents a zero and no change.  Two Fudge dice produce numbers in the range -2 to +2.