I run games that I have affectionately termed "Big Damn Heroes Roleplaying" after a line in Firefly.  Player Characters roll 4d6 drop the lowest die roll, SEVEN times, and drop the lowest total. Arranged to taste.  Moreover, if a player is unsatisfied with their rolls they can opt to reroll.  Even though 5e allows for stats to be increases over time, a lot of games do not get to past level 9, moreover the use of the optional FEATS systems takes the place of ASI, so having PCs with scores in the range of 10-18 doesn't bother me.  I, in fact, enjoy it.

I am probably going to get a lot of flak for this. I am old school. I have been playing D&D since Basic Edition. As a matter of fact, I think I still have a couple of the original dice. But, I digress.

In campaigns, the PCs (Player Characters) are supposed to be heroes. They are supposed to be awe inspiring (depending on their alignment), or even feared. I remember one campaign,  back in the 1980s, where we had made it to in the realms of 20th level (And we started at level 1). We had gotten to the point where we owned keeps, towers, and were revered, held in awe, had lands that we had divvied to those we felt deserved it, and one of us had even delved into, criminality, cruelty, and turned into a villain, but the rest of the party had to kind of ignore it because that character was part of the party.

With that being said, over the years I have seen many ways that people roll up their characters. I have even seen DM's just tell people "Here are your stats, get over it". D&D is supposed to above all else, be fun and enjoyable. And with the thought of PCs being heroes in mind, I have a few ways that I let people choose from when rolling up PCs. I do not use a point buy, array, or set stats. I have always said that a hero should never have a score lower than 9, period (unless something happens to the PC after the campaign has started).

I had not thought about everyone getting the same stat rolls before, and we always roll up PCs on Day 1 (Or since character creation can take so long, some consider it Day 0) as a group so the entire group can cheer, laugh, groan, or whatever at the dice rolls. And always remember, the DM has the last say so. If he/she doesn't like it, he can always change things. Below find the ways I like.

Riskiest - 6xd20 (Re-roll below 9). Place them in any order (Or do 1 at a time and go straight down the line), yes it is possible to start with a 20 before racial bonus in my campaign.

2nd Riskiest - d12+6 (Re-roll below 3)

4xd6 (Re-roll 1s and 2s) Drop 1

This one is my favorite:

24d6 (re-roll 1s and 2s) drop 6 dice. This leaves 18 dice with minimum 3 for your pool. Pick any 3 dice for a stat. Once those dice have been used, remove them from the pool.

That last one is pretty interesting, kind like a point buy dice setup...  interdasting.

Quote from Chivalrous2112 >>

 

This one is my favorite:

24d6 (re-roll 1s and 2s) drop 6 dice. This leaves 18 dice with minimum 3 for your pool. Pick any 3 dice for a stat. Once those dice have been used, remove them from the pool.

I can see why.  That actually sounds really cool.

I usually do a variant of the 4D6 where you reroll any 1s you roll once. If the dice show 2 ones in a row the dice gods want that to be a one. 

However i once ran a campaign where the PCs were meant to be overpowered so we did a 4D6 keep all 4 reroll untill no ones were showing.

I suggest 4d6 reroll 1s, minimum of 8 in each ability, and total ability roll of 69 to 75.  If player rolls 68, add one point to eligible stat, if rolls 76, subtract one point, etc.

I've considered rolling stats in pairs (you get to pick which pair), something like:

Roll 3d6. Use this for one of the two picked attributes (you can decide after rolling). The other is determined based on the value of the first:

• 3 -> 18
• 4-5 -> 17
• 6-7 -> 16
• 8-9 -> 15
• 10-11 -> 14
• 12 -> 13
• 13 -> 12
• 14 -> 11
• 15 -> 9
• 16 -> 7
• 17 -> 5
• 18 -> 3

Median attribute value is 12.5, which is about the same as 4d6 keep 3 or the standard array.

Quote from Chivalrous2112 >>

24d6 (re-roll 1s and 2s) drop 6 dice. This leaves 18 dice with minimum 3 for your pool. Pick any 3 dice for a stat. Once those dice have been used, remove them from the pool.

At that point, why bother rolling dice? 

Quote from Wysperra >>

Quote from Chivalrous2112 >>

24d6 (re-roll 1s and 2s) drop 6 dice. This leaves 18 dice with minimum 3 for your pool. Pick any 3 dice for a stat. Once those dice have been used, remove them from the pool.

 

At that point, why bother rolling dice? 

As I said, PCs are supposed to be heroes above all else. While yes, this does result in higher stats, you still have the chance at minimum 9s. And a couple stats at 18, but the majority of stats should be around 15/16 ish. After reading it again. I should have said you have to use 3 dice per stat.

After thinking about it, you could use the 24d6 (re-roll 1s and 2s) drop 6 method. And then the 18 dice you have left is your pool that the entire party gets to choose from. Remembering that you have to use 3 dice per stat, that gives minimum 9, max 18. And each  PC uses the same pool of dice. Makes it so each PC can tailor their stats as they see fit, yet each PC has the same total stat points to distribute. This would alleviate the complaints about one PC having super high stats and others low.

And then of course you could always skip the re-roll 1s and 2s if you don't like the idea of minimum 9. You are the DM, it's your game. 

The issue with a dice pool is that it's significantly better to focus on one stat and have the others lower than to spread between multiple stats, so someone with one stat very high should compensate by having a lower average.

The other problem is... what is the purpose of rolling for stats? In general I see it as being a chance to get an unexpected character, and if you can pick where all the dice go, that doesn't give you that.

Quote from Chivalrous2112 >> 

As I said, PCs are supposed to be heroes above all else. While yes, this does result in higher stats, you still have the chance at minimum 9s. And a couple stats at 18, but the majority of stats should be around 15/16 ish. After reading it again. I should have said you have to use 3 dice per stat.

That was the point of my comment. You're going to end up with two 18s two-ish 15s and two 10s. Just hand that out and don't bother rolling. 

The point of a roll is having a random element for good AND bad rolls. 

My current preference is for an adjusted point buy, with 37 rather than 27 points available, and the option to purchase stats as high as 17.  Cost is same as the PHB by memory, with 16 costing 11 and a 17 cost of 14.  I prefer this method or a comparative stat array.  Player Characters are Heroes, exceptional individuals that break the mold.  Standard array / 25 point buy is for weak, boring campaigns where barbarians wield forks - salad forks at that.

Quote from SergeTroy >>

My current preference is for an adjusted point buy, with 37 rather than 27 points available, and the option to purchase stats as high as 17.  Cost is same as the PHB by memory, with 16 costing 11 and a 17 cost of 14.  I prefer this method or a comparative stat array.  Player Characters are Heroes, exceptional individuals that break the mold.  Standard array / 25 point buy is for weak, boring campaigns where barbarians wield forks - salad forks at that.

Why? Standard array is still generally higher than you get out of NPCs.

Quote from SergeTroy >>

 Standard array / 25 point buy is for weak, boring campaigns where barbarians wield forks - salad forks at that.

 The success or failure of a campaign should not ride upon the stats of the heroes. 

Sad to say I disagree with you both, and based upon the manner of ability score generation most groups prefer (just take a look at the ridiculous numbers presented in Critical Role campaigns) I'd say the greater community does as well.  Welcome to the game.

The problem with stat escalation is that standard array PCs are already overpowered relative to nominally level-appropriate challenges, so giving more points means you're going to have to significantly boost every encounter, run with below-level characters, or accept the PCs facerolling every encounter.

Roll 4d6 6 times, reroll ones once.

Not true.  Firstly, I find the monsters to be incredibly weak even for the 25 point buy in a well adjusted party.  Just as I would adjust the players to make them more effective, so would I adjust the monsters where they needed it.  This is a very standard practice.  How do you think Critical Role works?  Mercer is not just occasionally introducing homebrewed monsters, he's also adjusting the stats and increasing both the difficulties and options available to the monsters the party encounters.  Any DM should underestand that their role comes with the option (and sometimes the necessity) to dabble in design.  After all, this isn't a video game that's locked against modding: modding is encouraged.

Quote from SergeTroy >>

Not true.  Firstly, I find the monsters to be incredibly weak even for the 25 point buy in a well adjusted party.  Just as I would adjust the players to make them more effective, so would I adjust the monsters where they needed it.

So... you boost the PCs, and then you boost the NPCs. What exactly did you gain from this exercise?