Level-Locked Loot

In games like MMORPGs, powerful items (looted or not) often come with additional character requirements that must be met before they can be used. These requirements—which can include level, class, stats, fame, and even karma—prevent players from purchasing massively overpowered gear and spoiling the challenge, and as such are the bane of the Munchkin.

Games with these do generally have a few rare and powerful items, which may actually be more powerful than a higher-level but more common item. The Infinity-1 Sword will almost certainly be such a weapon, although the Infinity+1 Sword is less likely to be. Such items are generally denoted with odd-colored Flavor Text or some similar effect.

Note: Since this is such a common trope, please only list aversions, subversions, or interesting variants.

Examples of Level-Locked Loot include:

Video Games

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 acess to it, it's annoying to receive unusable equipment as a quest reward.

MMORPGs

Rohan Online allows players to wear much higher level equipment but imposes stat penalties that may end up making the gear less powerful than what the player is qualified to wear.
Vindictus has the usual class and level restrictions, and also has a set of Proficiency skills that allow you to use higher-grade gear of a particular type (e.g. battle scythes, plate armor, secondary weapons, etc.)
Mabinogi mostly averts this, relying on price or difficulty ofacquisition to keep the heavy stuff out of the wimps' hands. A lot of gear is species-specific, though.
- Also, many enchantment effects activate at a certain level, and if you rebirth they become dormant until you reach that level again. Enchantment-effect triggers can also involve age and skill rank.
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.

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.
Freelancer has Level Locked Ships, with mightier ships capable of mounting more and better weapons, as well as having better power supplies. The Infinity Plus One Guns can only be installed on the three highest-level ships.
Knights of the Old Republic: There aren't any level restrictions, but there are a few items that can only be used by a light- or dark-side character.
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.
Somewhat averted in The Elder Scrolls Four as weapon/spell/armor effectiveness scales with relevant Skills.
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, 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.

Fighting Games

Dissidia Final Fantasy has this. All armors and weapons have a Character Level requirement. Similarly, accessories are ranked, from D to Star, the ranking indicating how many of one accessory can be equipped. For example, the player can equip but one Star-rank accessory, but two A-rank accessories, and so on. Mind, this is strictly player-only, since The Computer Is a Cheating Bastard.
- 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.

Web Comics

Parodied in reference to an announced Dungeon Siege film in Penny Arcade, shown here.
VG Cats demonstrate how it "works".
Virtual Shackles illustrate one of more dubious requirements.