Quick answer: Magic (blue) items roll exactly one prefix and/or one suffix; rare (yellow) items roll 2–6 affixes with at most three prefixes and three suffixes. An affix can only spawn when its affix level (alvl) is within reach of the item's ilvl, and ilvl equals the level of the monster that dropped it. The most-wanted magic-only rolls are Jeweler's (4 sockets), Cruel (+201–300% Enhanced Damage), +3 skill-tree prefixes, and of the Whale (+81–100 Life).

What are magic affixes?

Affixes are the random bonus properties that appear on magic and rare items. A prefix goes before the item's name (Cruel, Jeweler's, Volcanic), a suffix goes after it (of the Whale, of the Magus). One item can carry both at once, which is how you get names like "Jeweler's Monarch of Deflecting."

Magic and rare items draw from the same affix pool — but an important slice of that pool is magic-only. The strongest socket, enhanced-damage and +3 skill-tree rolls can never appear on rares, which is why top-end blue items (JMOD shields, +3 skill amulets) trade for real value. Every affix also lists which item types it can spawn on and at what level, so the pool shrinks or grows depending on the base item.

How many affixes can an item roll?

The item's quality decides the budget, and the rules are fixed (per Blizzard's Arreat Summit):

Affix level (alvl) and item level: what can spawn where

Every affix has a level requirement of its own — the affix level. When a monster drops an item, the game randomly picks among the affixes allowed on that base whose level is at most ilvl + 2, and the item's ilvl equals the level of the monster that dropped it. Higher-level monsters literally unlock new affixes.

Magic-only affixes worth knowing

These rolls can appear on magic items but never on rares. If you see one of them on a blue item, stop and check it before you vendor it:

AffixEffectAffix levelAppears on
Mechanic's / Artisan's / Jeweler'sAdds 1–2 / 3 / 4 sockets10 / 33 / 55Body armor, helms, shields, weapons
Cruel+201–300% Enhanced Damage51Weapons
Volcanic / Powered / etc.+3 to a single skill tree (class-restricted)60Class items, amulets, circlets
Godly+101–200% Enhanced Defense45Any armor
of the Whale+81–100 to Life50Body armor, belts, amulets, barbarian helms, circlets
of Vita+41–45 to Life91Grand charms
Ruby+31–40% Enhanced Damage66Jewels

The famous combinations come from pairing these with a strong suffix: Jeweler's + of Deflecting on a Monarch (JMOD), or a +3 skill-tree prefix with +20% Faster Cast Rate on a circlet — possible only because rares are capped at +2 to class skills while magic items can roll +3 to a single tree.

Best affixes by item slot

Weapons

Cruel (+201–300% ED, magic-only) is the ceiling for raw damage; Grandmaster's (+151–250 AR, +101–150% ED) is the top magic/rare AR-plus-ED prefix; Fool's adds attack rating and max damage that scale with character level. Caster weapons want of the Magus (+20% Faster Cast Rate) on staves, rods and orbs.

Armor, helms and shields

Jeweler's (4 sockets) turns a good base into a runeword-grade piece; Godly (+101–200% Enhanced Defense) is the defense ceiling. On shields, of Deflecting (+20% block chance, +30% faster block rate) anchors JMOD, and Chromatic adds +21–30% to all resistances.

Circlets, amulets and rings

Arch-Angel's-style prefixes give +2 to all class skills (alvl 90 on amulets and circlets, magic and rare), while +3 single-tree prefixes are magic-only. For casters, of the Apprentice (+10% FCR) appears on rings and amulets, of the Magus (+20% FCR) on circlets. Magic find lives here too: Fortuitous adds up to +15% MF on rings, amulets and circlets — see the Magic Find guide.

Charms

Grand charms roll "+1 to a skill tree" prefixes (the famous "skillers", alvl 50) and of Vita up to +45 Life (alvl 91) — a skiller with +40+ life is a top-tier charm. Small charms want Shimmering (+3–5% all resistances), high max damage/attack rating/life combinations, or Pestilent of Anthrax poison. Sunder charms are a separate unique tier — covered in Sunder Charms.

Jewels

Magic jewels roll the heaviest single mods: Ruby (+31–40% ED, magic-only) and Scintillating (+11–15% all resistances). Rare jewels can package up to four affixes at once, which is how the famous ED/res-all/IAS combinations happen.

How to get the affixes you want

Because ilvl equals monster level, farming high-level areas — above all Terror Zones — is the only way to access the top of the affix table. Beyond raw drops, three levers matter: