What are the equipment restrictions for NPC/Hirelings in Diablo 2?

Mercenaries follow the following sets of equipment rules:

Act 1 - Rogue Scouts

Armor, Helms, Bows (NOT crossbows or Amazon specific bows)

Act 2 - Desert Mercenaries

Armor, Helms, Spears or Polearms (NOT Amazon specific spears)

Act 3 - Ironwolves

Armor, Helms, Shields, 1 handed swords

Note that the Ironwolves do not actually physically attack with the sword, so finding one with good casting stats for whatever element you choose is is a better idea than finding one with good weapon damage.

Act 5 - Barbarians

Armor, Helms, Barbarian class specific helms, Swords (both 2h and 1h variety, though they cannot dual wield)

Also note that Mercenaries follow STR/DEX requirements for items as well as level, though generally speaking this is not usually an issue.

Those Hirelings are also known as Mercenaries. As listed on Diablowiki.net only the weapon and off-hand slots have restrictions as followed:

Rouge Scouts (Act I)

• Only Bows (NO Crossbows or Amazon only Bows)
• can use Cold Arrow or Fire Arrow in addition to Inner Sight

Desert Mercenaries (Act II)

• Spears, Javelins and Polearms (no Amazon only equipment)
• use Jab Attack and have a Aura dependent on type and difficulty they were bought in:

. |Normal/Hell|Nightmare | Combat |Prayer |Thorns | Offense|Blessed Aim|Might | Defense|Defiance |Holy Freeze|

Iron Wolves (Act III)

• Shield and Sword

• skills depend on type:

  Inferno or Fireball for Fire
  Glacial Spike, Ice Blast, Frozen Armor for Cold
  Charged Bolt and Lightning Bolt for Lightning

• they will not hit much with the sword - look for caster-bonus on it (for example, Spirit runeword)!

Barbarians (Act V)

• Barbarian class-specific items, one sword (no dual-wielding)
• use Bash and Stun

Additionally to the type restrictions, mercenaries follow the items requirements for Strength, Dexterity and Level. Back when I played Diablo II, act II Mercenaries were the most common choice due to their buff-auras.