Kingdom of Loathing has stat requirements for equipment, but in the earlier days of the game, there were no such requirements for consumables. This made it possible to skip from level 1 to level 4 immediately after a New Game+ by simply eating some of the best food in the game at the time, so it was eventually Nerfed by adding level requirements for consumables.
World of Warcraft restricts both gear and consumables by level. Yes, this means your character needs to learn how to eat anything besides stale bread and tough jerky. Averted with specific items meant to facilitate the levelling of alts which can be handed down from a high to low level character, but even those don't give you more stats than a good level-appropriate level gear piece would because they scale with character's level and increase in stats only when you do. The upside is, you don't need to upgrade them until maximum level.
A few items are actually unusable AFTER you reach specific levels. These are typically remnants of buff mechanics from previous expansions, such as sharpening stones, wizard oils and drums, which were discontinued in new content due to complaints about excessive grinding required to obtain them. Thus they cannot be used in content that isn't balanced around them being available.
Final Fantasy XIV has all gear locked to certain levels in order to prevent new players from acquiring powerful equipment from their friends and using them to blow through the early parts of the game.
The Secret World has gear restricted by skill points invested in the relevant weapons and talismans. Higher level gear has higher skill point requirements.
Role Playing Games
FATE and Torchlight both have a whole slew of character, stat and feat requirements for any equip you care to name, and the Legendary gear in FATE also requires a high Fame level. It's possible to remove an item and have several others unequip themselves because they were depending on its stat bonuses...and in your adventuring career this will happen at least once.
In Fable, it's possible to carry and even equip a weapon you don't have enough Physique for, but if you do so you end up dragging it laboriously along the ground and being completely ineffectual in combat.
In Phantasy Star Online the different kinds of items are restricted by different stats: armor is level-restricted, blade weapons are restricted by your attack strength, guns are restricted by your accuracy, and wands are restricted by your mental strength. Your other equipment is counted for the limit, so if you equip an item that increases your accuracy you can equip better guns than you normally could.
Do note you only need the stats when equipping the weapon. It wasn't uncommon for players to carry around crappy weapons that gave a decent boost to a stat for the sole purpose of replacing it with a weapon they didn't have the stats for yet.
Demon's Souls has a variant in which stats, not levels, are used to determine the ability to effectively wield weapons. It makes sense, really, since anyone could pick up a bastard sword, but not everyone will have the strength to swing it around one-handed.
In Diablo II, items do have level restrictions, and some items have strength requirements. These requirements can be slightly reduced in-game if the item has the special suffix 'of Freedom' or if it is socketed with a jewel that grants the same suffix.
Diablo III has "reduced level requirement" as a possible random ability on some gear, making level 60 kit that you can wield at (say) level 46 that still has the stats of level 60. The gap between 46 and 60 is a lot bigger than that between 32 and 46...
In Summoner, ability to use weapons is dependent on whether to character has the right weapon skill (and whether it's explicitly character-restricted), but gear for everyone but Rosalind is also dependent on their Heavy Arms skill.
Dark Souls, much like its spiritual predecessor Demon's Souls, uses stats to determine the effectiveness of weapons. Any player can equip any weapon, but if the player character doesn't have the minimum stats to properly wield it that weapon's performance will be severely penalized.
In Dragon Age: Origins, armor and most weapons have strength requirements. Daggers and bows have dexterity requirement instead. Some equipment is also restricted to specific classes or specializations, and some personal items are restricted to specific characters (including the Player Character).
Dragon Age II had two-stat requirements (e.g. strength and dexterity for swords and armor) but because most loot in the game scaled with the player's level, you would rarely pick up items that you couldn't use right away or within a single level-up.
In Rogue Galaxy, all weapons have a minimum character level, but by the time you can purchase a given weapon in the local shop, you will probably already be at a high enough level to use it anyway.
Fallout: New Vegas has a slight twist on the trope: you can use weapons tiered above your skill level or strength level, but this causes a penalty to range weapons accuracynote With free aim this means more Sniper Scope Sway, while VATS takes a direct penalty. The given skill level is what's required for maximum accuracy, though more skill will still increase the damage you do. and non-range weapon attack speed proportional to how far below the requirements you are. In both this and Fallout 3, you need to undergo the requisite training to use Power Armor, which generally doesn't occur until late in the game.
In Path of Exile, equipment can have not only level requirements but also Strength, Dexterity, or Intelligence requirements. Yes, this means that it is possible for a character to not be smart enough to wear a pair of witch's boots (maybe the lacing is really complicated?).
The sequel simplified the level requirements: instead of having nearly every level represented, there are now five tiers of equipment: Level 1, level 30, level 60, level 90, and level 100
Real Time Strategy
Dawn of War 2 usually has level requirements for equipping gear.
In UFO: Aftershock, there are certain types of equipment that require special training before soldiers can use them. For example, a soldier can't use rocket launchers until he gets the Trooper Level 1 training.
Borderlands: With the level cap now at 69 and having 2 play-throughs, not to mention, 6 bazillion guns, this game has loads of stuff you can't use yet.
Dead Island has weapons that can only be used at certain levels. While it's usually only one level too high by the time you gain access to it, it's annoying to receive unusable equipment as a quest reward.
The later Fall Out games had level-locked equipment after it was revealed in the first game that, with a bit of luck, you could charge nigh-naked into the final town of the game and obtain the best armor available before doing a single quest.