I.. have a complicated setup, but it works well for me. I have two stereo outs from my computer, one from the built in sound card and one from my audio interface. I'm considering finding a cheapish USB soundcard for a third out so I can separate system/game sounds from music and from voice. I have league and music going through the built in card and voice coms going out through the audio interface (thinking about it, it might be better fidelity wise to flip that) into channels 1-4 respectively on my mixer (1,3 panned left, 2,4 panned right). I have those channels set to go out through my group bus and the stereo bus. I also have a microphone for the stereo bus and I have the monitor settings to monitor the group bus (so I don't have to listen to the sound of my own voice other than to set mic levels). This is setup so that I can have the most control over levels when I stream (unfortunately, since I've moved, my internet is not good enough to stream...thank you uverse).
Those of you who don't get to hear any sounds from the game, you're limiting yourself in two ways. 1: there's a lot of audio cues in the game that can help alert you to what's happening in game, for example pings (though they can get annoying if someone is spamming them >_>), but also things like, say you're standing near your tower in top lane, but you're watching bot lane in case you need to teleport, since you're not watching your character, you don't see the emblem over your head that warwick is near and smells you at lower health (I'm assuming you'd be able to do something bot lane with lower health [you're a tank or something idk]), but if you had sound effects enabled (and the ww was silly and didn't disable his E), you'd hear ww howl. Plus, I don't know how you can go through life not having heard the satisfying noise of a Nidalee spear hitting its target or the great noise when you land a Mundo cleaver.