I personally am very much against a villain turning good after a speech from the good guy. There are some times where it actually can make sense, but I'll get to that later. Right now, I first need to explain why it is a problem.
The real problem with a villain being TNJ'd into turning good is that it ruins the villains character and as a result, hurts the story as a whole. Therefore it can be said that if it does not ruin the villains character, it might not be so bad.
Situations where TNJ was not bad (this is of course debatable)
-Zabuza: Zabuza never "turned good". He didn't stop being vicious and murderous. Rather, he just came to realize how much he cared for Haku.
-Gaara: Gaara was never "evil", not really. He was traumatized and basically insane. He was basically just taking out his hatred and pain on other people. Naruto managed to identify with him and show him that friendship is how to get rid of the pain that Gaara was feeling.
-Sasuke: Sasuke was also not really "evil". He was just taking out his hatred. Furthermore, his "TNJ" was gradual and therefore a part of his character development, and so does not ruin his character. Furthermore he most probably didn't even completely "turn good" yet.
Situations where a villain turning good is bad:
-Nagato: This was completely ridiculous. Nagato firmly believed that what he was doing was right and was steeped in is philosophy. All Naruto did was tell Nagato to believe him him and for no logical reason, Nagato abandoned his former ideology and decided to turn good.
-Orochimaru: I don't need to explain this....
-Obito: Basically the same reason as Nagato. Obito had developed an ideology of despair, and firmly believed that IT is the only way to save the world. He views Naruto as Naive. He is not insane like Gaara was because he has a very specific and complex ideoloy; he is not just taking out his anger. His change was not based on logical character development like Sasuke. There is no reason based on what I've seen for Obito to turn good. He is too far down his path to suddenly switch sides.
Some hypothetical reasons why TNJ might be bad
Some people might say it is childish and immature. While villains turning good is something that occurs in more childish stories, this is not such a strong reason. Logically a political solution should be considered more "mature" and simply killing your enemies would be immature.
Some people want to see intense action scenes and think that a villain should be killed in an epic battle. However this is simply a matter of preference. If you want to read a manga where the villains are just killed, that there are plenty of other manga you could be reading. Not everything has to be settled with a fight scene.
A villain being TNJ'd sometimes ca ruin all the character(s) have accomplished in order to finally defeat the villain. This problem is usually resolved since a villain is rarely TNJ'd until he is defeated in battle, and the implication is that the villain needed to be defeated in order to be TNJ'ed
Some people want to see intense action scenes and think that a villain should be killed in an epic battle. However this is simply a matter of preference. If you want to read a manga where the villains are just killed, that there are plenty of other manga you could be reading. Not everything has to be settled with a fight scene.
A villain being TNJ'd sometimes ca ruin all the character(s) have accomplished in order to finally defeat the villain. This problem is usually resolved since a villain is rarely TNJ'd until he is defeated in battle, and the implication is that the villain needed to be defeated in order to be TNJ'ed
The real problem with a villain being TNJ'd into turning good is that it ruins the villains character and as a result, hurts the story as a whole. Therefore it can be said that if it does not ruin the villains character, it might not be so bad.
Situations where TNJ was not bad (this is of course debatable)
-Zabuza: Zabuza never "turned good". He didn't stop being vicious and murderous. Rather, he just came to realize how much he cared for Haku.
-Gaara: Gaara was never "evil", not really. He was traumatized and basically insane. He was basically just taking out his hatred and pain on other people. Naruto managed to identify with him and show him that friendship is how to get rid of the pain that Gaara was feeling.
-Sasuke: Sasuke was also not really "evil". He was just taking out his hatred. Furthermore, his "TNJ" was gradual and therefore a part of his character development, and so does not ruin his character. Furthermore he most probably didn't even completely "turn good" yet.
Situations where a villain turning good is bad:
-Nagato: This was completely ridiculous. Nagato firmly believed that what he was doing was right and was steeped in is philosophy. All Naruto did was tell Nagato to believe him him and for no logical reason, Nagato abandoned his former ideology and decided to turn good.
-Orochimaru: I don't need to explain this....
-Obito: Basically the same reason as Nagato. Obito had developed an ideology of despair, and firmly believed that IT is the only way to save the world. He views Naruto as Naive. He is not insane like Gaara was because he has a very specific and complex ideoloy; he is not just taking out his anger. His change was not based on logical character development like Sasuke. There is no reason based on what I've seen for Obito to turn good. He is too far down his path to suddenly switch sides.