Maybe "edge" is too strong a word, but "helping hand" seems so lame ;)
In my AD&D campaigns, it was roll 3 sets of 4d6 (best 3 of 4) and keep the set you wanted. The DM got to keep the discarded sets as handy dice arrays for NPCs.
I also gave max HP at first level (I hated to see TPKs at any level, let alone first due to bad HP rolls), and counted rolled 1s as 2s for later HP rolls.
Of course, this was all learned after allowing players to use the Unearthed Arcana Stat Generation Aberration. Used it once - the horror!
So, what little house rules do you throw in to give PCs in your campaigns a slight edge?