A couple of weeks ago I saw a video about rolling characters the old-school way, 3d6, in order. It was really refreshing to see someone defend his point of view and could support his claim with solid reasons. I liked how Noah told examples of making the best of the worst, and he was also very thorough about this topic, with many great ideas.
My view is very similar, I have rolled 3d6 in order a few times and those were my most loved characters. It was fun to come up with a reason for those one or two poor stats I got. As an example, when I was playing Rappan Athuk a few years back and rolled my character the classic way, I rolled 18 Strength but a Constitution of 7. Quite contradicting to say the least. So I came up with the idea of a barbarian who had to take a magical potion upon his rite of passage, which granted him superb might, however, it left his health damaged quite a bit (and also his intellect, since I rolled an 8 for that). It was fun playing him, with bulging muscles but only with a primal cunning and stamina issues. He did really well and didn’t die, it was a great session with some good laughs.
I like to have my players roll up characters as well, although I’m a bit more lenient with the method. For Rappan Athuk I had them roll 3d6, in order, but I let them roll all 1-s again, and let them have two series of rolls and choose the better one. Now thinking about it, I may have been too nice. Still, two players got a 6 for their Charisma, which is not much of a big problem usally, but they still went ahead and tried to come up with a good reason for that score. All the other stats were pretty decent, and with racial bonus they could even feel powerful with good main stats for their classes.
I have noticed as well that many players are afraid of just going with such a gambit, and prefer to use point buy, or choose to play another system. I understand them, they don’t want their characters to suck (at anything, usually), since the character is usually our fantasy badass version whom we like to see succeed, overcoming obstacles confidently, and so on. Fortunately after a while most players get mature enough and want to mix things up a bit and then the miracle happens: they want to do 3d6, in order. That’s usually the point when roleplaying improves for many players (or even roll-playing becomes role-playing). I have also been through this “journey”, playing it safe, then after a while I just got bored with always playing “the same character class” and decided to go with rolling characters instead of point-buy.
As a DM, I like rolling up my NPCs as well, it can help giving them a little more personality, maybe even a weak spot or a defining feature which the players will remember them by. Of course it would be too time consuming to do this for every single one, but I found it a good method to spice my campaign up a bit with such NPCs. In my current Rappan Athuk campaign I’m running, Rex the Henchman is such an NPC.
I think the most important thing a DM needs to do is to convince his players to give 3d6 a try, and help them with ideas how to explain a bad stat, let them feel that it’s not the end of the world if they have an ability score of 6. Of course, if half of the abilities are at -2 modifier scores, a wise DM would let the player roll a new series…