DMG p136 defines attunement but doesn't give a concrete reason as to why an item might require it.

I can see a handful of reasons a magic item may require attunement vs. not requiring it, however, this is mostly meta-game speculation as to the designer's intent for the attunement mechanic. I don't believe the attunement property in WOTC magic items is so black and white. Here are some basic reasons I can see for requiring attunement:

1. It's stronger/rarer than an item without attunement. Many times the difference between a really good magic item and a standard one is whether it requires attunement. It's not a prerequisite, but there is a loose correlation amongst the WOTC magic items. I don't think a Pole of Angling is useful enough to require attunement, but a ring of Djinni Summoning is.

2. To limit the number of powerful items a player can have at the same time. Most PC's have 3 attunement slots max, although in some cases, such as a high-level artificer, a player can have more. If the magic item is rare and powerful, requiring attunement makes using the item a decision for the player at higher levels, when they may not have a free attunement slot.

3. To limit how quickly a player can equip/don a different magic item. Attunement requires an hour, so it limits a player's advantages during an encounter or time-sensitive sequence of events. If the item is so powerful that it grants a strong ability or get-out-of-jail-free card, requiring attunement means the player can't swap it during combat to insta-kill a specific monster type, immediately fly to escape fall damage, suddenly resist fire instead of cold damage because they put on a different ring when preparing items that morning, etc.

4. You don't know what it is until you identify it. If you're not a wizard, a cheap, but potentially risky way of identifying a magic item is to spend the hour to attune to it and see what it does. What you learn may be limited by your DM, but I tend to add the item directly to a player's character sheet if they decide to attune to it.

5. It's cursed. Most PC's won't attune to a magic sword if they know it's cursed. Attunement creates a bond with the item that potentially can't be broken without a cost. It also comes in handy to have a psychic bond to the item so the demon trapped inside the sword can communicate with the PC.

The above considerations help when creating your own homebrew magic items. But, I think the more important question is when to waive the attunement property for a magic item. 

Edit: A couple of items that break the mold are ones that are mechanical more than strictly magical or items that are not worn or carried. For the first example: Charlatan's Die vs. Deck of Illusions. The die seems more mechanical, while the deck is more magical, yet the die requires attunement and the deck does not. Second example: magical tattoos. The Masquerade Tattoo requires attunement, while the Spellwrought Tattoo does not. There are probably better examples, but these are what I found with a quick search.

Looks like there are about 300 magic items not requiring attunement and over 400 requiring attunement.  

Just on a cursory level it seems power level may be one factor, among others.  Wands work identically from what I can tell on a quick glance.  Wand of Magic Missiles doesn't require attunement, but Wand of Lighting Bolts and Wand of Viscid Globs do.  Wands mostly, but not all, often replicate spell effects so there may be some assignation of attunement requirement based on power level.

That last thought does work in line with the DMG's guidelines for creating magic items:

Attunement

Decide whether the item requires a character to be attuned to it to use its properties. Use these rules of thumb to help you decide:

• If having all the characters in a party pass an item around to gain its lasting benefits would be disruptive, the item should require attunement.
• If the item grants a bonus that other items also grant, it’s a good idea to require attunement so that characters don’t try to collect too many of those items.

So the guidelines in the DMG are fuzzy and basically ask for the DMG to be mindfully considerate of ramification if the item were literally up for grabs to all party members and also to be wary of stacking effects.  That may be all there is to the design philosophy.  Of course there may well be a more structured codified way of WotC designing magic items in house; but I imagine given the interest in homebrewing for public consumption WotC would have provided that structure in a Sage Advice column by now.

I think one of the major reasons to switch it like this is because of previous editions where you could get situations of a single character hauling around an armory's worth of different magical weapons for every situation: this way encourages players to pick a few powerful items instead.

I think if you're running a intentionally low magic game, your all magic items (except disposables like potions, scrolls, and some tattoos etc) requiring attunement doesn't seem particularly offensive or burdensome to game sensibilities.  Also provides good role playing bond making.  Say if a character has a +1 sword and upgrades to a +2 or +3.  What does the character do with the detuned +1 weapon?  It would be quite an honor or bargaining chip perhaps to grant it to a trusted contact or a donation to a religious order etc.   

I'm pretty sure in the DMG there's guidance to rarity and power level and when characters should have access to them.  Relatedly there are the tiered magic items grow in power with the character (I thought this was a Mercer innovation but there's precedent in other editions weapons one legacy and such).  With those guidelines I think DMs of "regular magic" or "high magic" campaigns to recognize that if characters at a certain power level have access to certain types of magic items, their adversaries should too.  

Quote from Vince_Snetterton >>

Quote from 6thLyranGuard >>

I think one of the major reasons to switch it like this is because of previous editions where you could get situations of a single character hauling around an armory's worth of different magical weapons for every situation: this way encourages players to pick a few powerful items instead.

 Yeah, I understand that.

I like to run a tougher game. Though I run a low magic game, eventually the players acquire quite a bit of magic. More and more, I am thinking that each and every magical item should require attunement. That likely flies against the philosophy of many DM's, and WOTC, but am considering it. Bottom line, the less magic in a game, the more the actual character's abilities and ASI choices matter. Given this is a player/char driven game, the more I become convinced that magical items should be limited by requiring attunement for each item.

 The simplest way to control the amount of magic items is to simply not have any magic shops exist. All magic items are found (e.g. from a previous civilisation), the skill to make magic items has been lost.

Which is something of the way 5E defaults to already.