Homebrew Standard Array:  {8,10,12,13,15,16}

Homebrew Rolling:  Everyone gets 8 and 16. Then roll 1d6+9 for each of the remaining four stats.

Homebrew Point Buy:  Starting array of {10,10,12,13,14,15}. Then add budget of 2 (maximum 16 allowed) and subtract budget of 2. This way, player can choose anything from the smallest possible spread of {11,11,12,13,13,14} to the largest possible spread of {8,10,12,13,15,16} while always totaling 74. 

Variant:  Allow player to further handicap a stat to 6.

I got this from the other DM my group normally plays with, and didn't change it because I didn't want to make everyone do a completely separate system just for me. But anyway, we use the "Roll 4d6 and drop the lowest (repeat 6 times)", except we do it 7 times and drop the lowest from that set. It ends up skewing higher than I would prefer, since I think weaknesses make the game more interesting.

My favorite was this method:

Step 1. Assign each stat a priority (Fighter says "Strength is my primary, Con is my secondary, Dex is my 3rd, Wisdom my 4th, Charisma my 5th, Int is my Dump").  Step 2.  Consult chart, Step 3. Roll appropriate Dice

Primary Stat:  14+1d4

Secondary Stat:  12 + 1d6

3rd Stat: 6 + 2d6

4th Stat: 3d6

5th Stat: 3d6

Dump Stat: 1d10+2

The advantages were:

1.  Assured everyone got at least 2 stats 13 or above.   Kept players happy, never had to re-roll
2.  Not everyone was min-maxed to the hilt.  You had Clerics that had an int of  12,  Wizards with a Charisma greater than their Con

Quote from Mog_Dracov >>

My favorite was this method:

Step 1. Assign each stat a priority (Fighter says "Strength is my primary, Con is my secondary, Dex is my 3rd, Wisdom my 4th, Charisma my 5th, Int is my Dump").  Step 2.  Consult chart, Step 3. Roll appropriate Dice

Primary Stat:  14+1d4

Secondary Stat:  12 + 1d6

3rd Stat: 6 + 2d6

4th Stat: 3d6

5th Stat: 3d6

Dump Stat: 1d10+2

The advantages were:

1.  Assured everyone got at least 2 stats 13 or above.   Kept players happy, never had to re-roll
2.  Not everyone was min-maxed to the hilt.  You had Clerics that had an int of  12,  Wizards with a Charisma greater than their Con

 I like it, but I would probably have to increase the minimum on the dump stat.  A score of 3 is low enough that it's a problem for the whole party, meaning it will largely define the character and a lot of the party's interactions.

You do 1d8+4, that has a minimum of 5.  I have played a Charisma 5 and it works as long as you let the Face of the party do the dealings.

I do 4d6 drop lowest, as point buy/standard array is a bit on the low side most of the time

I have really only GMed and gotten to play twice. As a player, the first time I did 4d6 drop the lowest. Which is fine I guess, I rolled pretty good so my character didn't feel so real to me. The other time I played, they 4d6 reroll 1s and drop the lowest. The result was a character with no stats lower than 12, which honestly was super boring, at that point my character was basically good at everything and I personally questioned why such a  person would even be an adventurer. Just go take over a nation or something.

I have a regular player that the three times I have said generate a character he does 4d6 drop lowest. But, he keeps rolling until he likes the numbers he wants. I personally find it really annoying, because at that point why not just make all of your stats 16 and just claim you rolled it? Why not just do that and not bother rolling? Why not just start with 20s in all stats? 

The whole point is to have things you are good at and things you are bad at. If your character is the best at 3 things, and better than average at the other 3, why even be in a party where your "weaknesses" are supposed to be covered? 

I guess some of it comes down to a power fantasy type of thing, and I am just a different person? I want a little bit of character development and opportunities for failure. My thought being that nobody laughs at all the times your character did something well or really even remembers it for that matter. Sometimes they do, but I would argue in that situation the GM created that situation for you, at least partially.

roll 4d6 keep highest 3, but re-roll 1's,

Quote from Mog_Dracov >>

My favorite was this method:

Step 1. Assign each stat a priority (Fighter says "Strength is my primary, Con is my secondary, Dex is my 3rd, Wisdom my 4th, Charisma my 5th, Int is my Dump").  Step 2.  Consult chart, Step 3. Roll appropriate Dice

Primary Stat:  14+1d4

Secondary Stat:  12 + 1d6

3rd Stat: 6 + 2d6

4th Stat: 3d6

5th Stat: 3d6

Dump Stat: 1d10+2

The advantages were:

1.  Assured everyone got at least 2 stats 13 or above.   Kept players happy, never had to re-roll
2.  Not everyone was min-maxed to the hilt.  You had Clerics that had an int of  12,  Wizards with a Charisma greater than their Con

This averages at like 16 15 13 10 7, which is actually a better selection then the standard point array, i might just make players use 16 15 13 10 7 in the next campaign

As a player, I would like to have the opportunity to do 4d6 drop x 6 method.  The reason for this is I doubt my DM would force me to keep anything below a seven.  As a result, I would expect to get a higher average and a higher chance of getting a spectacular primary and secondary stat.  BUT ...

These things have to be understood in context.  If you do the 4d6 drop x 6 method some players in the campaign are going to get really good stats and others will hopefully get a character build that by itself makes them feel good.  But eventually many parties are going to fall into the dilemma that one or two players are dominating the RP and strategy encounters and the other players will feel left out.  If all the players have the maturity to handle that then it will work out but I fear often there will be stat-envy.

Because of this, as a DM I would tell the players we are going to use point buy.

Each player rolls 4d6 six times, dropping the lowest from each roll.  The results from all the players are then pooled together, and we have a draft.  When a player’s turn comes around, they choose one score from the remaining draft pool.  To keep things reasonably balanced, we go Player 1, 2, 3, 3, 2, 1, etc... 

Quote from MarcellusFadingDusk >>

Each player rolls 4d6 six times, dropping the lowest from each roll.  The results from all the players are then pooled together, and we have a draft.  When a player’s turn comes around, they choose one score from the remaining draft pool.  To keep things reasonably balanced, we go Player 1, 2, 3, 3, 2, 1, etc... 

 That sounds like a really bad idea, personally.  You can forget playing anything even remotely MAD in that context, like a Monk or an Eldritch Knight.  You're also starting Session 0 pitting your players against one another over who does and doesn't get high numbers.

Quote from drag0n_77 >>

That sounds like a really bad idea, personally.  You can forget playing anything even remotely MAD in that context, like a Monk or an Eldritch Knight.  You're also starting Session 0 pitting your players against one another over who does and doesn't get high numbers.

It isn't pitting players against one another, other than someone deciding they feel like being weak. I've never understood the purpose of random stats that you can arrange in your choice of order, though; randomly rolling some weird stat combo might give me unusual ideas for a concept, but if you can reorder them it's really just a matter of 'are the stats good or bad'.

I give the choice of point-buy or rolling.

For rolling I go with the 4D6 dropping the lowest number 6 times and the player arranges them as he/she wants. If the rolls are bad, the player can roll another 4D6 to replace the worst one.

Some players enjoy the randomness of the rolls, the last session 0 they were very excited about the rolls. I personally don't like it because it unbalances the party, the group I'm running now has one character with everything between 10-13 except Constitution, so it's not really good on doing anything besides taking damage.

For me, I use custom standard array [10, 11, 12, 13, 14, 15] or point buy with 30 point.

My very first game from when I was a kid we did roll 3d6 in order and went with it. Not my favourite although I loved that character.

Now: I like a modified standard array of 15 17 13 12 10 8

Or one I made up for my home game was:

have all the players roll a Collective total of 18d6, plus 1 additional d6 each. (Ie: if you have 6 players they each roll 4 dice. 2 players they each roll 10 did) Next each player drops the lowest dice they rolled leaving you with 18d6. Those 18 dice rolls is each players dice pool for stats. Pick and choose any 3 dice for each stat and add em up. Removing any dice you use. Everyone rolls, all have access to the same dice for balance and you can get a wide variety of combinations of stats. I also tell my players that at the end to have no stats below 6 but they self regulate pretty well. No one wants a 3 in a stat.

We do 4d6 drop the lowest, but we roll three sets of 6 and choose which of the 3 sets we like.  I just rolled a new character today and ended up with 17, 16, 14, 13, 10, 7. I had the choice of a slightly better set, but went with this set went well with the character concept I have in mind.

It is because we roll this way that we tend to have characters that actually get to take Feats. Standard Array and Point Buy can make that hard to do depending on the character concept you have in mind.

Quote from Golaryn >>

We do 4d6 drop the lowest, but we roll three sets of 6 and choose which of the 3 sets we like.  I just rolled a new character today and ended up with 17, 16, 14, 13, 10, 7. I had the choice of a slightly better set, but went with this set went well with the character concept I have in mind.

It is because we roll this way that we tend to have characters that actually get to take Feats. Standard Array and Point Buy can make that hard to do depending on the character concept you have in mind.

 I just make 1 side quest were the player can get 1 feats of their choice. In some campaign, during session 0 I would just give them them the chance to take a feats.

this just my way. 

I was taught 6d6, re-roll 1s and add the top 3? 

Quote from Mania_71 >>

I was taught 6d6, re-roll 1s and add the top 3? 

 That would give you a crazy high set of stats ...

You have an 8% chance to roll an 18, and less than a 1% chance to roll either a 6, 7 or 8.  And all that is before racial modifiers.  I bet you get some great characters with some great feats.

Good luck.