Well, Ive had a few ideas brewing for a while. Some of them Ive tried myself, some of them are still in the planning stage (and have been for the last year or so

). I hope that maybe someone will try them out.
1. Holy Cow
Cows are holy to our civilization. We seek to protect them and nurture them at all costs. Through out the game, we must obey the following rules:
- Our cows (cows with in our culture border) must never be disturbed, no units, not even workers, are allowed to set foot on the cow tiles.
- We seek to free all cows in the world from field labor. We must pillage all tile improvements from every cow tiles on the map, and also keep those cows from being exploited ever again. This must be done before we can win the game. Our units are allowed to stay on the cow tiles while performing this duty.
- We must win by the UN!
This is just a fun little variant. Its not meant to be hard. The only challenge comes from trying to carry out those free cow operations without angering our AI neighbors too much as to prevent our UN win.
The players are encouraged to be creative when it comes to freeing the cows. Try to use as many off-beat methods as possible. Got a unit that you never used before? Can you herd all the cows (occupying the cow tiles) using only Elephants?
Of course, this variant is best served using India with a super all cow start
2. Kingdom of the Clowns
One very simple rule: -- every city must contain at least one entertainer.
Yep, starting from the very first city, the first citizen must be turned into a clown.
The early game will play very differently from your normal games. Settler factories? Forget about it! City sites will also have to be planned carefully to avoid size-zero cities

.
Of course, with most slow start games, military is often the best solution. I have tried this variant in a solo game. A warmonger will have a lot less trouble with this variant, but if you try to play peacefully
This variant is much easier with a AGR civ on a fresh water start, though a none-AGR civ with a food bonus start is also possible (think about it, how

)
3. Out of Options
In civ, there are two general classes of strategies: the warmongers and the peaceful builders. The warmongers build units and try to conquer the world, while the peaceful builders build improvements and try to out research the world. So what if you take away both of those options
There are two very simple rules:
1) You may never build any city improvements.
2) You may never attack a city.
Any tactics not forbidden by those two rules (and not forbidden by the usual SG exploit list) are allowed. This means, for example, if you want culture, you have to build the ToA (no capturing, remember). If you want to capture cities, you can try propaganda.
This variant is very hard, though not impossible at low-enough levels. I recommend that you develop a plan before you start, and then try to stick to it.