From Nookipedia, the Animal Crossing wiki.
Katrina (ハッケミィ, Hakkemii) is a blue female panther, with dark purple eye makeup and bright orange eyes. She can tell the player their fortune, and appears in all Animal Crossing games. In Animal Crossing she has a male voice like Gracie and Saharah (who are both male in Japan), but in Animal Crossing: Wild World and Animal Crossing: City Folk she has a female voice.
 In Animal Forest
 In Animal Crossing
In the original Animal Crossing, Katrina's tent will appear randomly in location and by date. She can tell the player their fortune for 50 Bells. Copper can let the player know when she will appear in their town a few days in advance. Her tent is open from 9:00 P.M. to 9:00 P.M. the next day. On New Year's Day, she will set up a desk by the Wishing Well, giving the player a letter with a fortune in it. The effects of the fortune last the rest of the day.
 In Animal Crossing: Wild World
In Wild World, Katrina's tent will appear randomly in front of Town Hall once a month. She can tell the player their fortune for 100 Bells. She can tell players about there love life, also. You can also get your spirit cleaned for 10,000 bells. She mainly has the same role as she does in The Original Animal Crossing.
 In Animal Crossing: City Folk
In City Folk, Katrina can be found in the city in the building furthest to the right. If you have told a villager your birthday she will greet the player by the player's star sign (e.g. if the player's birthday is on March 15th, she will call the player a Pisces). She can tell the player their fortune which can last a week, and/or she can give the player a charm for that month, usually involving strange tasks. However, the player who is given the fortune cannot obtain the charm - the task stated by Katrina needs to be done by a visiting player and only they may obtain the charm. One would have to cooperate with a friend to do the prescribed tasks in each other's towns to obtain the charm. No matter what the player asks her to do, she will have something drop on their head. It will make the player wobble and be "dizzy" (stars appear around the character's head).
The below fortunes are the responses given by Katrina to the player. These are also followed by the effects.