Reputation

From Nookipedia, the Animal Crossing wiki

Reputation is a mechanic in Animal Crossing: City Folk and Animal Crossing: New Leaf that keeps track of actions that a player does in the game. When completing an activity a high number of times, the player will develop a reputation amongst the villagers in town for that action, bestowing a unique title upon them. While villagers spread rumors about it amongst themselves, they will occasionally pass it along to the player in order to inform them of their reputation.

Villagers can also spread rumors about another player's reputation, particularly when visiting other towns, or when a villager has moved from another player's town.

In City Folk

Several reputations in City Folk can be gained by simply wearing certain clothing or accessories regularly. Others require in-game actions to completed many times before they can be gained.

Reputation Requirements
Angelface Wear the Halo accessory regularly.
Bridezilla Wear Bride Look clothing regularly.
Witchlette Wear clothing from Gracie's Magical Look fashion line.
Four-Eyes Wear glasses accessories regularly.
Parasol Girl Equip umbrellas regularly.
Fishing Fan Obtained by catching fish regularly.
Flyswatter Obtained by catching insects regularly.
Bloom Bud
Flower Girl
Plant and water many flowers (500+).
Tree Shaker Shake trees regularly.
Pro Listener Fulfil villager requests regularly.
Average Joe Trade items with villagers regularly.
Party Peep Talk to villagers regularly and have high friendship with them.
Broke Joker Obtained by rarely socializing with villagers.
Early Bird Obtained by playing mostly in the morning.
Raindrop Obtained by playing mostly when it rains in the game.
World Traveler Travel to lots of other players' towns.
Bell Hoarder Obtained by having many Bells deposited in the bank, while spending very little.

In New Leaf

New Leaf introduces many more reputations, but almost all of them can now only be gained from completing in-game activities many times.

Reputation Requirements
Freshman Mayor Obtained upon becoming mayor. This reputation cannot be regained after gaining another reputation.
New Face Obtained upon moving into town. This reputation cannot be regained after gaining another reputation.
World Traveler Travel to lots of other players' towns.
Time Traveler Obtained by adjusting the in-game clock regularly.
Pro Traveler Visit other players' towns regularly.
Happy Tourist Go on tours on Tortimer Island regularly.
Stump Maker Chop down many trees with an axe.
Pro Listener Fulfil villager requests regularly.
Aspiring Designer Create lots of designs, and have many villagers in town wear them.
Fish-and-Bug Star Catch and donate to the Museum many different kinds of fish and insects.
Deep Diver Catch all types of deep sea creatures.
Fishing Expert Catch all types of fish.
Bug Whisperer Catch all types of insects.
Bellionaire Obtained by having 1,000,000 Bells or more deposited in a savings account.
Shopaholic Purchase items from shops regularly.
Civic Leader Build Public Works Projects or enact Ordinances regulary (contributing money to PWPs often also counts)
Fashionista Pass Gracie's fashion check regularly.
Tree Hugger Plant many trees regularly.
Green Thumb Breed many kinds of hybrid flowers.
Flower Fan Plant and water many flowers (500+). Picking up flowers and setting them back down contribute towards this total.
Fishing Fiend Obtained by catching many fish regularly.
Fly Swatter Obtained by catching insects regularly.
Diving Fan Obtained by catching deep sea creatures regularly.
Bell Pincher Obtained by having many Bells deposited in the bank, while spending very little.
Social Butterfly Talk to villagers regularly and have high friendship with them.
Favor Doer
Good Neighbor
Hometown Hero Obtained by maintaining a perfect town rating.
Individual Obtained by rarely socializing with villagers.