There are a lot of ways to figure out a characters ability scores. If you are old school then you probably use the first method, rolling 3d6 (Probably in order, though some generous DMs allow for arranging to taste). If you are more new school you probably roll 4d6 and arrange them however you want. A third method that has become popular in the last few years is point-buy, where you get a pool and invest the points from your pool into your various stats.
Personally I've used the first two methods and always found them to work well. I don't, and I don't think I ever will, play with point-buy. It just lends itself too much to cookie cutter characters. Characters with the same class have more or less the same array of stats to accommodate a certain "build" instead of being unique.
Another options that I recently read about on Grognardia that I was unaware of is a percentage based chart like the one used in FGU's Space Opera. Rather than rolling the traditional d6s, player break out their percentile dice and roll on a chart that favors higher numbers. Additionally players have a number of points they can allocate toward certain stats based on their class. It's a very interesting approach.
A percentage based chart really gives you an exceptional amount of flexibility. I think that is what intrigues me most about it. Using multiple small dice you are going to see a traditional bell curve but with this the probability curve can be whatever you want it to do. What's more each individual statistic can have its own unique curve.
That was what I set out to do when I made a preliminary version that I might consider using in a future campaign. I wanted certain statistics, Constitution especially, to have a higher basement. The idea is that with rampant disease, starvation, and other hardships anyone with less than an 8 con died off. Other statistics, like Intelligence also see an increased minimum because those who would only be a burden to their families are often cast out and allowed to perish. Infantcide is an accepted practice and if a father finds the baby deformed, inferior, weak, or if he suspects that he may not be the father, it is a generally accepted practice that the child would be abandon in the wood and left to die of exposure. All of this horror and death adds up to higher minimum statistics for starting characters.
Here is my first attempt:
It obviously needs work, and I'm not sure that I'd like to keep all of them as near normal bell shaped curves. Again, it's the flexibility that I find intriguing about this method. One could have a separate chart like this for each race, eliminating the need for bonuses and penalties for each race since it would be built right in. Though I wouldn't play with the first attempt I think it warrants further attempts. With a tweak here and a tweak there I think this method could work out really well.