Anything that does elemental damage (flame, shock, cold). So thundering presence will for example, Mage's Fury, even your Twilight does shock damage. Anything that's magic damage (crystal frags, for example) won't. Force Siphon is a way to get magicka return on all attacks though rather than just elemental. Check the tooltips for what type of damage it is - anything elemental will work.
Only Mage's Fury, Bolt Escape and Overload will trigger elemental drain.
Lightning form and lightning splash will not proc it and also pets will not proc anything. I've tested this a lot. And also lightning staff heavy attack channels won't restore anything, only the final projectile.
Wall of Elements does not
Destructive Touch DoT does not
Elemental Ring DoT does not
Same goes for Force Siphon
It's safe to say, that Elemental drain is quite a joke actually.
Even Scalding Rune does not...
Force Pulse (destro staff morph of force shock) does indeed trigger the drain. Without drain I'm out of magicka in about 55 seconds (34k magicka, 900 regen). With drain magicka bar never moves. I am, of course, one of the surprisingly small pool of sorcs that does the force pulse/light attack weave to proc fragments... So I can see why so many people think it's useless.
In PvE, if I see you spamming mage's fury when not in execute or using curse, I laugh. You're doing no DPS. Sure you have shiny numbers for spell damage, but my 2150 spell damage yields 6k+ force pulses plus 2.1k (all unbuffed) light attacks each cast. Mage's fury does what, 2,700 damage at 2600+ spell damage?
In sum, it works spectaculary with force pulse. Never run out of magicka.
Cue the blah blah but my overloads hit for blah blah. While you're overloading my meteor is hitting for 70k over 12 seconds while I'm spamming pulse/light attack and shards per procs. (Entropy right before meteor = 20% spel damage buff and 20% overall damage buff on ice comet). If the boss is a mover, my arty comes to play or I just swap to overload