It really sounds like a good idea, the question is just what type of handicap do u give for which rating difference? And how do you adjust the ratings for wins or loses?
Handicapping systems - levelling the playing field

The Wikipedia article discusses several forms of handicapping:
#1. Draw Odds - where a draw is counted as a win for the weaker player - doesn't even affect the playing controls during the game.
#2. Removing a piece or pieces from the stronger player is easy to implement! It could just be done as an extension to the set of possible starting positions when starting a game.
#3. Giving the weaker player some extra moves at certain points (in the style of 'Bisques' in Croquet) requires a major implementation change - and fundamentally alters the nature of the game.
#4. Capped pawn and Ringed piece are interesting - but require major implementation effort.
Starting a piece down is the easiest to implement. You would offer this handicap to another player simply by selecting that start position - in precisely the same way that you can currently offer someone a disadvantagous opening!
(If we also take up buttonc's suggestion that any non-standard opening is automatically noted in the Notes; this may prevent disputes later.)
Should an assisted win count in a player's statistics? No. Perhaps there should be a new category: Won/Lost/Drawn/Unscored.

Unrated games are ALREADY not counted in Wins, Losses and Draws - so no new category is called for.
A handicapped starting position (assisted game) should be forced into the Unrated category.
Another form of handicap:
#5. Hidden piece(s)/partial blindfold. Hide one or more of the stronger players pieces from him. This has already been implemented seemingly... http://www.chess.com/forum/view/help-support/black-horses-have-disappeared

In a rated game on chess.com there are already draw odds. By stalemate the highest ranked player loses more points!

Good point, CeGi. Are there any plans to be able to see the rating Adjustment from the opponent's point of view?

Another form of handicap:
#6. Swap sides with your opponent (when in a disastrous position). You may need to do this more than once!

#7. At a point in the game, when the weaker player is fairly certain to lose, the stronger player must accurately forecast how many moves to checkmate. If he doesn't achieve checkmate in precisely that number of moves (strong form) or no more than that number of moves (weak form), it is counted as a win for the weaker player. Since Fritz (so I am told) is able to detect mate in 23, this should not be too great a handicap for a really strong player.
This is not restricted to forced mates. It adds a bit of spice to the endgame and can be thought of as an alternative to resignation in a friendly game.

#8. The stronger player must move each different type of piece in turn: pawn, knight, bishop, rook, queen, king - on successive moves. If he is unable to move the appropriate piece, then the next piece in the sequence is moved (and so on).
A simpler form is that no single piece may be moved twice in successive moves.

I think it would be great if we could choose any starting position for unrated games, it would enable :
-> a position with handicap
-> playing simpler chess (for example games with only 8 pawns and 1 piece), to train with finals
-> training with original openings
-> ...

Were you planning to insist on a king on each side? If not, that would be quite a substantial handicap!

Hi. Sounds good but to me it takes the edge off the game. I personally think that rated games are more fun because you are playing top improve your rating and have to think more carefully. Regards Phil R.

Some games have too much edge to start with. I played a series of 11 games against someone rated 100 .. 300 above me - and lost them all. After being given a selection of increasing advantages, it gave me (false) hope that I might one day beat him.
These handicapping schemes apply equally outside chess.com. When playing a person (perhaps a younger family member) who is just learning the game, they provide a structured framework. If you can assess the advantage numerically (as Wikipedia does with its schemes), you arrive at a scale for determining how well a player is progressing.

It isn't supposed to be fun. Chess is supposed to be: blood, sweat and tears - or possibly, blood, toil, tears and sweat (and disaster). Have you got The Right Stuff?

SUMMARY - for those who don't like reading entire discussion:
These handicapping schemes apply equally outside chess.com. When playing a person (perhaps a younger family member) who is just learning the game, they provide a structured framework. If you can assess the advantage numerically (as Wikipedia does with its schemes), you arrive at a scale for determining how well a player is progressing.
The Wikipedia article discusses several forms of handicapping:
Starting a piece down is the easiest to implement. You would offer this handicap to another player simply by selecting that start position - in precisely the same way that you can currently offer someone a disadvantagous opening!
(If we also take up buttonc's suggestion that any non-standard opening is automatically noted in the Notes; this may prevent disputes later.)
A handicapped starting position (assisted game) should be forced into the Unrated category.
If you need help, please contact our Help and Support team.
How many players would be interested in using handicapping systems (see http://en.wikipedia.org/wiki/Chess_handicap ) for unrated games in chess.com?