I've always been a big fan of the IDEA of Dungeons and Dragons (and by extension, Role Playing in general). But every time I've tried to play it I've been disappointed.
I just had an idea which is likely a summary of many past ideas I've had about D&D- basically something that could be played on a long car ride or something. I'll call it D&D Travel Edition for now ;)
Basically an RPG where the DM does normal DM stuff. However, instead of rolling dice to determine stuff, the DM simply decides if an action succeeds and to what extent.
The game would be story based, so if the action messes up the story then the DM would have to figure out a way to work around it, or the action may not be possible or fail or something. For example, say a character is suspicious of the King's Visir and does some kind of detect magic and notices that he's got the king under a charm spell... maybe it turns out that this is the main plot and the characters weren't supposed to figure it out until later... but now they know so the DM has to deal with that. Furthermore, say that character gets mad about it and attacks the Visir where he stands (behind the throne, in public, etc)... the DM might have to stop him so as not to kill the rest of the game- maybe the King's guards jump in the way and grab the guy. Either he slips away or they drag him to prison, either way the party is now on the outs with the court.
This is the kind of D&D I always wanted to play. I find the normal dicefest gets bogged down in rules and combats.
There are many diceless roleplaying games (free form rpgs), however if you want to have a random dice-like element to the game one could use numberplates of cars as the source of randomness (a bit like spot-o actually).