League-of-legends – Does item effects stack with other item effects

You can stack items, however any unique properties will only apply once. Some stats stack differently than others (math) but they ultimately do stack.

For example, Madred's Bloodrazor provides the following:

+30 Attack Damage
+40% Attack Speed
+25 Armor

UNIQUE - On hit, deals Magic Damage equal to 4% of the target's maximum Health.

Buying more than one of these will give you the additional attack damage, attack speed and armor, but not an additional unique effect (4% of target's health per hit).

You can have more than one unique effect, but you may only have one of each unique effect. There are no items that cancel each other out.

Boots are a specific case. You can't have more than one movement buff from any kinds of boots at all.

As for other items with UNIQUE passives, as long as you don't have the exact same item, they all stack on top of each other.

Apparently, there are other exceptions as well. From the wiki:

Unique effects that do not cumulate among differents items include Movement Speed effects from boots (only the best effect applies), proc effect of Sheen, Lich Bane and Trinity Force, and the mana gained from Tear of the Goddess, Manamune and Archangel's Staff.