Stick the accuracy mod on the Geth Plasma Shotgun and it hits nearly all the time, even at range.
Just wait until your reticule goes red, fire (or charge up then release when it goes red) and the projectiles will tighten up and fly towards tracking it as it moves (unless it dodges, in which case they will probably miss). If you fire when it isn't red then the projectiles won't group together and will be more spread out.
I really like using it because it is very powerful, fires quickly, has a fair amount of ammo and can hit targets at medium to long ranges. I couldn't handle it at first but you get used to it.