This প্রবন্ধ 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 প্রশ্ন 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 জনপ্রিয় 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 জনপ্রিয় one, with the heavy arguments and discussions all over, it remains as a জনপ্রিয় one of all time. Friendly discussions are often seen.
Misty, May and Dawn

4. "Ash is still a 10 বছর old"
With Ash Ketchum remaining 10 after the 15 years of the anime, why would this not be a জনপ্রিয় topic xD অনুরাগী 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 জনপ্রিয় one. "Which one came first?" would be the most repeated প্রশ্ন here.

6.) Bring Misty back!
The original girl leaving the জীবন্ত was really very sad especially for the Misty fans. Petitions were hold দ্বারা অনুরাগী to bring her back, don't know what results the petitions had but many অনুরাগী 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 জনপ্রিয় topic. 'Imagination' would be the main activity i guess. The most জনপ্রিয় 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 প্রণয় the Pokérap? xD আপনি might প্রণয় the other generation Pokemon আরো but agree অথবা not, the original 151 Pokemon were the best! These Pokemon were and are in trend!

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

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

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