There doesn't seem to be a consistent rule here. The best I can come up with is an item requires attunement if its rarity is Rare, Very Rare, or Legendary, and it provides a permanent bonus (not consumable or limited daily use).
Unfortunately, there are exceptions to this. The Mace of Smiting is Rare but doesn't require attunement. The Cloak of Protection is Uncommon, but does.
The guides for sentient item creation and artifact creation mention nothing on attunement, but all of the sample items require it.
However, the rules for custom magic items on DMG 284-5 do mention attunement. All they have to give is general advice. The first suggestion is to use attunement to prevent player abuse of bonuses: no mage-handing your Boots of Springing and Striding back over the gorge to the next party member to attempt the jump. The second suggestion is to require attunement for bonuses that are both common and desirable. You can only attune three things at once, so you can't simultaneously stack defensive bonuses from your Ring of Protection, Cloak of Protection, Armor of Invulnerability, and Arrow-Catching Shield all at once.
As an addendum, you should check out the Modifying an Item section on DMG 284. Specifically, I believe all three items you mention have near-equivalents that you can use as templates.