Misty: She left the gym to her sisters, and they still operate it, with a little help from her occasionally.  She still has her Pokemon (including Psyduck, who still hasn't evolved).  And, like I said, she married Ash and they had kids.

Brock: He became a Pokemon breeder, and he still has the gym, but his daughter Petra operates it most of the time.  And he married Susie (the one who gave him Vulpix, remember?), and like I just mentioned, they had one child, Petra, but when she leaves he takes care of the gym again.

Jessie and James: They got fired from Team Rocket, but Butch and Cassidy let them back on the team again when Giovanni retired.  They had one son, Clyde, who also became a member of Team Rocket.

Butch and Cassidy: They escaped from jail and stayed with Team Rocket, and their hard work paid off because when Giovanni retired Cassidy became the boss, with Butch as second in command.  Oh yeah, and they had a daughter, Bonnie.

Gary: He married Giselle (from the episode about Pokemon Tech), and she made a living as a model, while he was a Pokemon researcher.  They had a daughter, Fawn.

Professor Oak: He's actually still alive, and he's still a professor, and he still gives young trainers their licenses.  Basically the same as before.

Bill: He's still a Pokemon researcher/collector/whatever, and he also has an advice column in a Pokemon magazine, where he advises trainers about how to raise their Pokemon and what TMs to teach them, when to let them evolve, etc.