So, a while back, I mentioned running a Planescape game - sadly, it died off after a while. Next plan is to resurrect these games, and run a proper real-life campaign.
However, I've started moving away from D20 systems. I feel that they're just too fiddly, and in some cases, more focused on all the number crunching and horrendous maths inherent in the system, rather than on the good bits - the characters. So I'm experimenting with a couple of different rules-light systems to try and get the real feel of Planescape, without losing too much of the good stuff (i.e. some of the D&D-isms, like alignment, that ended up becoming major forces within the game).
So, my two front runners are Risus and FATE.
Now, Risus I have posted about before - it's awesome, fun, and light as all Hell. You make characters based around clichés - so, for Planescape, Plane of Origin, Race, Alignment, and Faction would be pretty good springboards for these.
These will tell you a bit about where your character is from - whether they're from the Howling Madness of Pandemonium, the hard-working plane of Bytopia, or the super-organised Mechanus, a lot about them will be determined here. You could also just be a native Sigilian, not aligned to any other part of the Great Wheel - but it still implies knowledge of the Cant, being clued-in, etc. Hell, Prime is perfect as a Cliché - one of The Great Clueless (i.e. those who are new to Sigil and the Planes in general) makes a good character (he used to be a farmer, now he's thrust into a world of time-travel and jetpack-powered apes!), especially for new players to The Planes (means they can pick it up as their character does!).
Plane of origin acts as a really good rider for a race cliché - while a Bytopian Dwarf will be stoic, hardworking and honest, an Ysgardian Dwarf will be a HERO OF BATTLE - all axes, heavy offence, etc. By the same token, an Ysgardian Elf will be a master swordsman, a cunning combatant, possibly even a Bladedancer. It adds a little bit of depth, and gives you more ways to use that cliché creatively.
Way, way back in Olden Times, you could be a Human, an Elf, a Dwarf, or a Halfling. And by all the Gods of Oerth, you liked it. Nowadays, with 4e, you can pick to be a demon-looking thing, a dragon-looking thing, or a giant-looking thing straight off the bat! Allow some other sources, you can become a zombie vampire with undead ancestors (I think, when you add it all up, you become 150% Undead - pretty goddamn impressive!).
But, you are still limited by one thing - game balance. You'll notice all the cool new things I talked about are "X-looking things". If your team consists of three primary school teachers, a housewife and Jason Statham in Crank, you have an imbalance. By the same token, playing a dragon in your usual gaming group will be fraught with problems (especially in D&D - they have flight, they're Large or bigger, and they have spellcasting. Goodbye, game - you were so nice until we broke you).
... But not Risus. Here, almost any cliché can be as flexible, if not more so, than something as powerful as a Dragon. Hell, with Risus, you can blow the racial choice wide open - you could be an Elf (any of the many, many varieties), Half Dragon, Genasi, reformed Pit Fiend, fallen Deva, a dying God... the only limit is your imagination, and how many dice you want to put into that Cliché.
Read any D&D book, find a race that appeals (whether they're PC races, monsters, whatever), figure out what that cliché would mean in game, and bam - you have your race. Little changes can make a big difference as well - Dwarven Runemaster, Dwarven Brewmaster, and Dorfy Dorfy Dwarf all bring something different to the table.
Planescape took Alignment from being a bit of a bugbear and an excuse to make Paladins fall, and made it a grand cosmic force. Hell, some of the creatures of the Outer Planes are literally made of Chaos, Law, Good, etc. So it can be pretty important. It also gives a two-word description of your average response to a situation.
From Lawful Good Boy Scouts, to Chaotic Evil puppy-bashers, people run the gamut of alignments. Think about your character on the classic axis:
Will they try and help people wherever they can? Only when it suits them? Only when it's the right thing to do, and not when the Law says so? Will they actively screw people over? Or just the really bad ones?
Factions make up the major political players in Sigil, and can make for some really interesting Clichés. Like the Sensates - try everything, once, for the path to true Enlightenment is through experience. Add Sensate to something like Chef, and you get a cook who'll cook anything, just to see how it tastes. He'll even throw in some right weird stuff, like Liquid Pain or magic mushrooms, on a whim, just to see what they're like and how they interact with the other flavours.
Guvnors run Sigil's legal system, and try to learn the Rules of the Cosmos - mainly so they can find the loopholes they can abuse. A Guvnor Lawyer can worm his way out of any contract, even if he has to break the laws of physics to do so. Hell, he might not even realise he's doing so - he thinks he's just that good.
The Doomguard follow entropy, and believe it is the natural fate of the Universe to die a slow and painful death - why not speed things up a bit? Brutal Doomguard Pessimist would be a classic. You could even have the Surprisingly Cheery Doomguard, who is pretty bright and happy despite his beliefs, and who will talk with great passion about the joys of Negative Energy and pessimism.
Read up on some of the Faction's philosophies, find which one looks most interesting, and think about how you can use it to further your idea for your character. Or how you can make someone who follows them, in an unusual way. Or how it would interact with their day-to-day life. Anything you can take from it and
Add in a few random ones like Bemused Planar Explorer, Mutinied Sky Pirate Captain, Real Mean Drunk, etc. and you're good to go. Each cliché should provide something for your character - each a little bit of backstory, a skill, or a character trait, hopefully all coming together to form a pretty good package.
And, in the interests of completeness, a few sample characters to get you thinking:
Rat-Bastard Tiefling Thief (4)
A Daemon with a Blade (3)
Decent Short-Order Cook (2)
Big Hit With the Ladies (1)
Raised on the mean streets of Sigil's Hive Ward, Varren is a right nasty basher - currently holding employ between cutting purses and chopping onions at The Laughing Paladin Inn's kitchen.
A Very, Very Lost Ranger (4)
Bow and Sword in True Accord (3)
On At Least Speaking Terms with the Animals (2)
Part-Time Herbalist (1)
Saman stumbled into Sigil while looking for the privvy in his local one night. He still hasn't found a way back, though he continues to look in between misadventures.
Bare Fisted Monk 
Strong-Minded Water Genasi (3)
Don't Think, DO (2)
Stupidly Arrogant (1)
Stupidly Arrogant (1)
Descended from the Elemental Plane of Water, Annalise takes her heritage very seriously- flow like Water, strike like Fire. Except Fire is dumb, so let's make it "flow like Water, strike like Water". You know, wetly.
Next time, we look at FATE, which is almost like Risus, but a lot more serious!