During the Kanto saga, the Orange Islands saga, and the majority of the Johto saga, Jessie, James, and Meowth were all excellent characters. They each had likable personalities and provided the series with great entertainment. However, I thought the inclusion of Wobuffet to their team in Johto was a mistake, since it is nothing more than a poor man's version of Misty's Psyduck.
Beginning with the final episodes of Master Quest, the quality of Jessie's character decreased. Jessie was usually portrayed in the final Master Quest episodes and the Hoenn saga as being entirely cold hearted and inconsiderate. While she was hot headed and could act selfishly in series' episodes prior to the final ones from Master Quest, she was still shown as having some redeeming character traits. For some reason or another, the writers of the series also started to make her appear very ignorant. She has never been the most knowledgable character from the series, but she was never as uninformed as she was in the final Master Quest episodes and the Hoenn saga. I also dislike how the writers decided to include her in contests, since they were one of the worst new features added to the series in the Hoenn saga (though Jessie was a more amusing rival than most of the other ones May had). James, who was depicted in the Kanto, Orange Islands, and Johto sagas as being an easy going and gentle guy, also became snippier mid-way through the Hoenn saga. And Meowth? In the Hoenn saga, he fizzled into the background and became nothing more than wallpaper, not unlike what happened to Brock and Misty during the Johto saga.
With the exception of "The Ole Berate and Switch," Jessie, James, and Meowth remained essentially the same during the Battle Frontier saga. In the Sinnoh saga, I have noticed that Jessie and James do sometimes go back to the ways they were before the writers decided to alter their characters. Alas, the same cannot be said for Meowth, who is still mostly a background character (I only remember him having an important role in "Noodles: Roamin' Off"). Unfortunately, James now also serves as a background character half the time. This usually occurs when Jessie is competing in contests.
My verdict:
Kanto: Got game
Orange Islands: Got game
Johto pre final Master Quest episodes: Got game
Final Master Quest episodes: Got game for James and Meowth. Lame for Jessie.
Hoenn: Lame
Battle Frontier: Lame
Sinnoh: Sometimes got game, but other times lame
If you are rating the trio solely on villainy, they were only villanious in "Pokemon Emergency." After that episode, they became comic relief villains, though they would still occassionally have villanious moments throughout the Kanto saga.