What is the most effective way for mages to fill empty soul gems without using a Soul Trap enchanted weapon? Any tips would be appreciated.

Use the spell that when enemy dies his soul is trapped.

I just use the soul trap spell hot keyed for fast access.

use the soul trap spell in one hand and a powerfull destruction spell in the other, and then go find animals and soul trap them, then kill them, i find horkers are the best way to do this, as there are plenty on the icey shores, otherwise fox's and wolves ect work fine, drauger also work some ruins can be a great place to fill alot of gems also.

Alas, it sound like a bit of process. I wish Skyrim had buff effects/passive abilities like Dragon Age. I thought the Soul Trap was associated with Bound Weapons, and it would do this automatically.

It's easy to do. I used it with I think my thief when I got vampirism.

I usually summon an atronach, have a follower who can also summon (with a staff), then hit a mammoth with soul trap, and we go to town on him. By "we", I mean they get beat up while I run away and occasionally fling a spell their way.