To a large extent the job of a game designer is to create rules, so it's obviously tempting to try to make games in which the players write the rules. That way we can kick back, relax and have a well deserved holiday.
The archetypical game in which the players are asked to create their own rules is probably Nomic, which you should look at the wikipedia page for if only to see the most and least useful game summary ever devised. Essentially play begins with a set of rules dictating how players vote on additions and modifications to the rules of the game, the only move being to propose and vote on these things. As play advances rules are added and the core of the game might mutate or be deleted entirely, until eventually someone wins under the terms stipulated by the rules that were voted through.
I've dipped my toes into the opaque waters of the game but have never engaged in particularly advanced play. I hesitate to call it a heavy game, as it could mutate into any sort of game, but the nature of the sort of person who's attracted to it seems to favour the development of complex and intricate systems. To an extent the game encourages this, as no player would vote for a motion that would allow another player to win and complexity makes it easier for players to obscure their intentions.
However it's entirely viable to generate a game in which players can moderate the rules that's more accessible:
At the start of a game of Fluxx, each turn players will draw a card and play a card. Many of these cards feature new rules, which will change how play goes. It's simple, accessible has brought joy to countless gamers and I hate it.
The experience is far more constrained the Nomic, in that players are never devising their own rules, but deciding which of the existing rules to put into play. These existing rules never quite generate enough depth of complexity to make the game interesting to me, generally changing very little and interacting infrequently. Still, I love the notion of a player modified ruleset being so accessible and I can appreciate the artistry that's gone into making that happen.
I can think of a game that's both entirely accessible and has almost completely player defined rules, though it's at best a sub-mechanic:
I have a complicated relationship with Wench, brought on by the tension between my design sensibilities and politics (culturetics?). I'm still waiting for someone to make an analogous game with a different theme (and periodically threatening to do it if I get the chance). It has executed on the free rule making fairly neatly though, the rule applies evenly to all players, there's a reason for there to be a divide between the person who's benefiting from it being broken and the person who conceived it. We have a couple of hours rules to exclude certain abuses but generally it works pretty well.
Except when someone decides on "Your name is the name of the player two seats to the left, if you respond to the wrong name you've broken the rule." at a gathering of people who've just met each other. I'm never forgiving her for that
Besides these three quite different examples of player lead rules manipulation there are plenty of others as well as games that become this if the rules are interpreted broadly enough. Munchkin comes to mind, in which the pre-errata Cheat card allowed a player to play a card that would normally be cheating. Applying that to cards that are illegal because they're from different games essentially winds up with a make it up as you go along game that bears only superficial resemblance to the original having been stitched together from other parts.
Thinking about the types of game that have used this mechanic and their strong and weak points, getting players to write the rules is far from a holiday and probably more of a headache than a traditional game. On the other hand the expression of creativity is one of the fundamental reasons to game, often overlooked in board games, so it feels like there's still plenty of untapped potential here. Something to work on another time perhaps.
Though perhaps wizard academy needs a promo spell that does something of this nature