This Статья contains opinionated view so this is/may not be factual.

In No particular order, here:

1. Ash and Red
Ash and Red
"Are they the same person?", the most common and the main discussion of this topic.
Though they are not but this Вопрос has always been raised. They are also compared in their Pokemon training skills.

2. Mew vs. Mewtwo
Another topic which has been heavily discussed. Mew vs. Mewtwo is one of the most Популярное Pokemon comparison. With Mewtwo clearly having higher base stats than Mew, and also the highest base stats of the Kanto region, the other side still holds good. It doesn't have an official conclusion of who's the stronger one i think.
Mew and Mewtwo from the first movie

3. Misty, May and Dawn
Pokegirls!! xD I don't think i need to say anything but anyways. This topic is no doubt a very Популярное one, with the heavy arguments and discussions all over, it remains as a Популярное one of all time. Friendly discussions are often seen.
Misty, May and Dawn

4. "Ash is still a 10 год old"
With Ash Ketchum remaining 10 after the 15 years of the anime, why would this not be a Популярное topic xD Фан assuming Ash's current age would be the main activity on this matter.
Ash Ketchum on episode 3

5.) Digimon vs. Pokemon
Personally, i hate this topic and see no reasons for comparison, what i see the most is bias. Only because there's "mon" in both don't mean they are comparable. Still, this topic is very active and indeed a Популярное one. "Which one came first?" would be the most repeated Вопрос here.

6.) Bring Misty back!
The original girl leaving the Аниме was really very sad especially for the Misty fans. Petitions were hold by Фаны to bring her back, don't know what results the petitions had but many Фаны still miss Misty. Though there's no probability of her returning as a main character but many re-appearances has been made.

7.) If Pokemon were real
Another Популярное topic. 'Imagination' would be the main activity i guess. The most Популярное related thing would be Smosh's "Pokemon In Real Life".
Smosh's Pokemon in real life

8.) 0riginal 151 Pokemon!
"Catch 'em, Catch 'em, Gotta Catch 'em all, Gotta Catch 'em all! Pokemon!" Who don't Любовь the Pokérap? xD Ты might Любовь the other generation Pokemon еще but agree или not, the original 151 Pokemon were the best! These Pokemon were and are in trend!

9.) Pokeshipping vs. Pearlshipping
Two most Популярное shippings of Pokemon! And the most Популярное that includes Ash Ketchum, so what do Ты expect? xD Both shippings are very Популярное among the fans. From various hints in the Аниме to songs like 'High Touch' performed by the seiyuus of Ash and Dawn themselves are taken into count.
Pokeshipping (Ash & Misty) and Pearlshipping (Ash & Dawn)

10.) Pikachu!
Пикачу is itself a very Популярное Pokemon topic. Its the most Избранное Pokemon all over. Even who don't know much about Pokemon, is sure to know Pikachu.

There maybe some еще but these are the ones which came to my mind =) would be glad to find some еще so do tell ;D