Ability Haste is the most common stat on completed items: 53 of 118, ahead of Attack Damage (44) and Ability Power (36)

I counted the stats on every completed item on Summoner's Rift, all 118 of them. The most common stat isn't Attack Damage or Ability Power. It's Ability Haste, on 53 items. That's 45% of the pool, ahead of Health (50) and Attack Damage (44), and about 1.5x as many as Ability Power (36).

What Ability Haste is

It's the stat that shortens ability cooldowns. The more you stack, the more often you can cast, and at 100 haste you cast exactly twice as often. All numbers come from Riot's official static data for patch 16.21. Completed items here means final-form items that don't build into anything else, including the 6 tier-two boots and the 5 final support items (honestly, I expected AD or AP to be the default stat on completed items).

How many items carry each stat

I also checked the top two together. 25 completed items have both Health and haste. Only 40 have neither, about a third of the pool. Two thirds of completed items carry Health, haste, or both.

Haste comes in only four values

Sort the 53 haste items by value and you get just four numbers: 10, 15, 20 and 25. The most common is 15 (24 items), then 10 (15) and 20 (11). The top value, 25, appears on only three items, and all three are AP items.

Item	Stats
Archangel's Staff	70 Ability Power, 600 Mana, 25 Ability Haste
Horizon Focus	75 Ability Power, 25 Ability Haste
Cosmic Drive	70 Ability Power, 350 Health, 25 Ability Haste, 4% Move Speed

AP items are more likely to have haste

Of the 36 items with Ability Power, 21 also have haste, 58%. Of the 44 with Attack Damage, it's 17, 39%. AP items are about 1.5x more likely to carry haste.

Crit is even more extreme. Of the 14 items with Critical Strike Chance, exactly one also has haste: Essence Reaver. That's 1 in 14, 7%. Crit items tend to pair with Attack Speed or Move Speed instead, and they're built almost as a separate family from haste (Yun Tal Wildarrows lists its crit chance as 0%, but I still counted it among the 14).

Three stats is the standard

Most completed items carry three stats: 66 items, 56%. 28 have two, 22 have four. Only two have a single stat: Rabadon's Deathcap (130 AP) and Swiftmarch (65 Move Speed). Outside of boots, Rabadon's is the only item that gets by on one stat. Fair enough, with 130 AP you don't need anything else.

The most Health on one item is Warmog's Armor at 1000, followed by Heartsteel at 900. Both carry only Health and Base Health Regen, no haste.

Takeaway

With haste on 45% of completed items, you pick some up no matter what you buy. Half of the Health items (25 of 50) and about 60% of AP items have it, so tanks and mages speed up their cooldowns without even trying. On the other hand, Essence Reaver is the only completed item that gives crit and haste in one slot, so crit builds have a hard time getting more ability uptime from items. Maybe that's why haste rarely comes up in ADC build talk: there's barely anything to choose from.

Source: Riot Games' official static data.

Haste is the most common stat at 53 items, yet only one of them stacks with crit. Maybe ADCs are just meant to spam auto attacks instead