I compiled a list of skill affixes for better readability. All of them are datamined, so they may be inaccurate. I only included the highest level affixes on the list.
All of the skill bonuses are suffixes, so only one can spawn on a Magic item. Rare items are a question mark in this regard, because we don't know enough about the item generator. It's possible, that the number of skill affixes is limited to one even on Rare items.
These affixes start appearing on class-specific items in Nightmare and on generic items in Hell. What's interesting is that some of the highest level affixes can't spawn on the most powerful class-specific items, because their item level isn't high enough, but they can spawn on the generic items with the highest level. For example, you can't get a 3 seconds duration extension for Blizzard on a Demi Lich, but a Sacred Shield may carry that bonus. I hope this will change.
Code:Item Group 1: Sources, Shields Item Group 2: Wizard Hats, Helms Item Group 3: Swords, Staves, Daggers, Spears, Wands, 2H Axes, 2H Swords, 2H Maces Skill Bonus May Spawn on Item Group Arcane Orb +2-8% Critical Chance 1 Arcane Torrent Arcane Power Cost Reduced by 1-5 2 Blizzard Duration increased by 1-3 seconds 1 Disintegrate Arcane Power Cost Reduced by 1-5 2 Electrocute +5-14% Inreased Damage 2 Energy Twister +2-8% Critical Chance 3 Explosive Blast +2-8% Critical Chance 2 Hydra Arcane Power Cost Reduced by 1-10 2 Magic Missile +5-14% Inreased Damage 3 Meteor Arcane Power Cost Reduced by 1-5 1 Ray of Frost +2-8% Critical Chance 2 Shock Pulse +5-14% Inreased Damage 1 Spectral Blade +5-14% Inreased Damage 1