My group generally uses point buy, but I tried out something new for a character in a solo campaign I'm running since there are no other players and I didn't have to worry about PC vs PC balance:
Use the standard array of 15, 14, 13, 12, 10, 8, arrange as desired, then roll 4d6 drop lowest in order, and use whichever is higher. The standard array is thus a safety net to ensure the PC gets good scores where the player wants them, and the 4d6 adds a random element to it, so a figher could end up with 18 Intelligence, for example.
In the solo campaign in question, the player was creating a paladin PC, and assigned the standard array as follows (please note that the player is not an experienced gamer to begin with, and is starting to get back into D&D again after some time, and so may not have made mechanically optimal choices):
Str 12
Dex 10
Con 8
Int 13
Wis 14
Cha 15
After rolling in order, the player got the scores in brackets, and the final abilities are as follows:
Str 12 [8] -> Str 12
Dex 10 [12] -> Dex 12
Con 8 [15] -> Con 15
Int 13 [13] -> Int 13
Wis 14 [18] -> Wis 18
Cha 15 [17] -> Cha 17
So, the player got lucky and rolled a 46-point PC with one 18 and one 17, and the "safety net" effectively added only another 4 points. The PC still looks pretty much like a paladin, although she probably ended up with a higher Wisdom and Constitution than the player would have assigned if character creation had been based on 4d6 drop lowest arrange as desired.