First of all, they meet requirements for perks and that's their most important role. Better Criticals for example requires PER and LCK at 6. Also they all give a bonus to associated skills, for example INT will boost Medicine. Those skills are listed in the game under each attribute so no confusion here. Luck gives a small skill boost across the board, +1 point to every skill there is. There also are sometimes very rarely raw SPECIAL checks in conversation, for example guard letting you pass "just because" if you have LCK 7 or recognizing someone's disguise if you have INT 8. There's one companion easier to recruit if you have INT 8 and there's one quest that I know of that can be completed via high CHA.
Strength - Carry weight, melee/unarmed damage bonus (+0.5 dmg per each point here)
Perception - Compass range for location markers and enemies, MINIMAL accuracy bonus (below 1% between PER 1->10)
Endurance - amount of implants, initial health, health per level, fatigue (how easy you are to knock down)
Charisma - 5% bonus to companion damage and armor per a point.
Intelligence - 0.5 skill point more per a point here (there's 90 skill points of difference between INT 1->10)
Agility - running speed, draw speed, reload speed, number of AP
Luck - 1% crit chance per each point here. This might not seem like much but remember many weapons multiply it meaning 1% here can as well be extra 5% with a sniper rifle. Also casinos win chances are strongly influenced.
My builds are either crazy dump stat builds - or extremely balanced ones.
For one example of a good general gunner build able to open all good perks and learn all the required skills (before implant -> after implant):
S 5 -> 6
P 5 -> 6
E 7 -> 8
C 4 -> 4
I 7 -> 8
A 5 -> 6
L 7 -> 8
Ah, you have said that agility can increase running speed, but I have heard from people that have tested 1 vs 10 agility.
They have said there is no difference. (or not enough to see anyway) Have you tested it, or checked the GECK?
Agility is the SPECIAL that I would really like to have the GECK stats for.
I plan on making a build based on a weapon, and keeping my agility tight, for my next play though.
Thinking of making a miss fortune/mysterious stranger vats spammer, with high critical chance.