Ash
Since he was a child, Ash has dreamed of becoming the World's Greatest Pokémon Master. When he turned ten-years old, he was allowed to receive his first Pokémon; however, because he over slept, Professor Oak, the local professor in Pallet Town, gave him Pikachu, the last available Pokémon at the lab.
Pikachu and Ash did not start off on the best of terms, but they quickly formed a bond and since then have been inseparable. Ash can be described as dense, reckless and naďve. He is and many more of those rather negative qualities, but just like any hero should, he has a wonderful spirit and heart. He never gives up even when a situation seems impossible – and, this strategy has proven to be successful, as he's always come out triumphant to some degree.
He shares a longtime rivalry with childhood friend, Gary Oak, the grandson of Prof. Oak. These two managed to get past some of their bitterness later on, but remain hardheaded rivals with each other and continue to strive to be better than the other.
Ash's mother, Delia, is supportive and loving, though she does tend to be clueless and lighthearted towards some of her son's achievements. His achievements are, in fact, very impressive: he's the winner of the Orange Islands tournament and Battle Frontier, and has earned very high rankings in the Johto, Hoenn and Indigo Leagues.
Although strong-willed and determined, Ash lacks independence. It's only been because of his traveling companions that he's achieved so much. He shares unique connections with each of his friends, even those he's known for a very short amount of time.
Ash has always had a very extraordinary team of Pokémon, which alters from region to region, save for Pikachu. He's caught over 40 Pokémon and continues to travel with hopes of fulfilling his dream. He's currently in Sinnoh.
Misty
Aspiring to become a Water Pokémon Master, Misty is the youngest of the Cerulean Sisters, who share ownership of the Cerulean Gym. Being the youngest, Misty puts up with a lot of slack from her older siblings, Daisy, Violet and Lily, who constantly torment her for not matching their skill and beauty. Truth be told, Misty is a far more talented trainer than her three sisters, no doubt a result of striving to be better than them in the first place.
Misty loves Water Pokémon more than anything. She is partial to them in all ways, but has a few exceptions here and there, most notably Gyrados. Even with her passionate love for Water Pokémon, she adores anything 'cute,' and is one of the many reasons she mothers over Togepi. Originally, having pushed Ash and Brock out of the way when Togepi's egg hatched, Misty's face was the first thing Togepi saw and hence instantly thought of her as its mother.
Misty has a big heart for Pokémon. She cares about what happens to them and how they are treated but despises Bug Pokémon with all her might. This negative attitude is not limited to Bug Pokémon either. Though compassionate, Misty is very stubborn and moody. She has a short temper and does not like to be demeaned by anyone.
When Misty was basically forced to go her separate way from Brock and Ash, she expressed difficulty and heartache for leaving her best friends. Misty resides at the Cerulean Gym, where she has officially claimed the title of Leader. She has grown quite a bit character-wise, regaining a sense of independence and uniqueness.
In the Chronicles side-series, she is seen taking care of the Gym and the Pokémon there. She no longer has Togepi, who she released into the Mirage Kingdom during a cameo appearance in Advanced Challenge.
Brock
Brock was the Gym Leader of Pewter City and caretaker of his nine brothers and sisters until he decided to travel with Ash. His father, Flint, began taking care of his siblings after he left Pewter City. He has expressed bitterness towards his mother, Lola, and father for their lack of attention and role in his life, but holds some respect for them.
As the Leader of the Pewter Gym, Brock originally trained only Rock Pokémon, but no longer chooses to be exclusive to one type. He dreams of becoming a Pokémon Breeder one day and therefore has owned a variety of types, some particularly special such as Vulpix and Bonsly.
Brock is a bit girl crazy and cannot help but flirt with every attractive woman that comes his way. His greatest crushes consist of every Officer Jenny and Nurse Joy he's encountered. Very rarely are his feelings returned, the biggest exceptions being Temaku from The Heartbreak of Brock and Lucy, one the Frontier Brains.
Brock has traveled everywhere with Ash except the Orange Islands. During the course of that journey, Brock stayed with Professor Ivy, another infatuation. He thrived to learn more about her work and abilities, but ultimately left due to mysterious circumstances which left him too scarred to even talk about. Since this incident, however, Brock has remained by Ash's side, traveling through Johto and Hoenn with him.
A loyal friend, Brock has always been somewhat of a mother figure to Ash and other traveling companions. He cooks and cleans for them, taking care of almost every vital aspect of traveling, including navigation.
He's currently in Sinnoh, still traveling with Ash.