STR: Determines the amount of stuff you can carry. Also affects the max potential damage you can do (very minor increase in damage).
STA: Determines your bonus HPs (can be signficant). Also determines the size of your endurance pool (used for combat skills). Used to be used to determine how fast you got tired when running or fighting, but that was removed in favor of the endurance pool system recently.
DEX: Determines your chance of a proc going off. Also has an affect on combat skill increases.
AGI: Minor effect on avoidance AC (very minor!). Also, *may* have an effect on defensive skill increases.
INT: Determines the size of your mana pool (int casters: wizard, necro, chanter, mage, shadowknight, bard?). Also provides a bonus to skill up chances for many skills (including trade skills).
WIS: Determines the size of your mana pool (wis casters: cleric, druid, shaman, ranger, paladin). Also provides a bonus to skill up chances for many skills (including trade skills).
CHA: Determines base prices that merchants will sell to you (adjusted by faction of course). Also has a minor effect on mind affecting spells (charms specifically). The vote is still out last I heard on whether cha affects mezzes or fears though.
Also note that trade skills often have an associated stat that affects skill up chances. Normally, the highest of wis or int will determine skill up chance. However depending on the skill, another skill may also be in effect if it's the highest. Smithing uses str and fletching uses dex for example. I have no idea about others though since I'm not much into tradeskills.
There's probably some other minor stuff, but that's the most important things to know.
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