From the Super Mario Wiki
Kleptos are California condors who attempt to steal Mario's hat in Shifting Sand Land during the events of Super Mario 64. Since then, they have continued to make infrequent appearances in the Mario series. Their name is a pun on kleptomania, the inability to resist theft.
Super Mario 64 / Super Mario 64 DS
When Mario first meets Klepto in Super Mario 64, he is holding a Power Star. Needing the star, Mario knocks the item out of the bird's grip and claims it for himself; therefore, Klepto's subsequent obsession with stealing Mario's hat could be a way of getting back at Mario for stealing his Power Star. Mario can attack the bird, knocking him out for short periods of time. Klepto, eventually, will regain his senses and continue trying to steal the hat. Without his hat, Mario takes more damage when attacked.
Klepto has the same Power Star and purpose in Super Mario 64 DS. He also appears in another level, the Sunshine Isles, accessible from the Rec Room. He makes a final appearance in Tiny-Huge Island, when the character is big. He is carrying, as usual, a star - except this time it's a Power Star. Additionally, though Klepto only steals heroes' caps, he will attack and cause harm if he glances Yoshi in the vicinity even if Yoshi uses any of the plumber's Caps.
In Mario Golf: Toadstool Tour many Kleptos can be seen flying in a desert stage. This confirms that Kleptos are a species, and that maybe the Kleptos Mario sees in each game are different from the one in Super Mario 64.
Mario Pinball Land 
Mario Party 4
Klepto also appears in Mario Party 4. He is used to transport characters to different spaces on the game board.
Mario Party 5
In Mario Party 5, it has its own orb, where, if landed on, Klepto will appear and take the character to another character's space determined by roulette. In the instruction guide, Klepto's name is erroneously spelled Clepto.
Mario Party 6
Mario Party Advance
In Mario Party Advance, a Klepto guards a treasure chest with a star. When the player arrives at Klepto's Ruins, his quest involves attempting to open the chest by entering the 4-digit code, giving them the hint that it is also his favorite word. When speaking, he has a tendency to stutter and repeat the word "for," indicating what the code is. By guessing the correct code (4444) and opening the chest, Klepto rewards the player with the Gaddget Map Maker. The ending states that Klepto changed the code to the treasure chest.
Mario Party 8