This article 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 question 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 popular 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 popular one, with the heavy arguments and discussions all over, it remains as a popular one of all time. Friendly discussions are often seen.
Misty, May and Dawn
4. "Ash is still a 10 year old"
With Ash Ketchum remaining 10 after the 15 years of the anime, why would this not be a popular topic xD Fan 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 popular one. "Which one came first?" would be the most repeated question here.
6.) Bring Misty back!
The original girl leaving the anime was really very sad especially for the Misty fans. Petitions were hold by fans to bring her back, don't know what results the petitions had but many fans 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 popular topic. 'Imagination' would be the main activity i guess. The most popular 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 love the Pokérap? xD You might love the other generation Pokemon more but agree or not, the original 151 Pokemon were the best! These Pokemon were and are in trend!
9.) Pokeshipping vs. Pearlshipping
Two most popular shippings of Pokemon! And the most popular that includes Ash Ketchum, so what do you expect? xD Both shippings are very popular among the fans. From various hints in the anime 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)
Pikachu is itself a very popular Pokemon topic. Its the most favorite Pokemon all over. Even who don't know much about Pokemon, is sure to know Pikachu.
There maybe some more but these are the ones which came to my mind =) would be glad to find some more so do tell ;D