Well, I'm not sure if we're counting the "was popular but now lagging" anime's and I'm also not sure what's popular right now... So I'll list the one's I like.
Majin Tantei Nougami Neuro (Demon Detective Nogami Neuro)
. The anime and the manga seriously branch off from each other but both tell pretty decent stories. I enjoyed it most from the strange angles, weird characters, and torture play.
. Still need to watch the anime but I've hit mangafox's latest update for the manga.
Loooved the crazy anime, still have to finish the manga.
. Read the manga, need to watch the anime.
. Love this manga. Don't think it's an anime yet.
. Manga was/is (not finished) awesome. The anime... deviated in tone and art style and not in a good way.
Tegami Bachi (Letter Bee)
. From the manga I have it's currently gorgeous and more interesting than most shoujo manga.
. OMG THIS MANGA NEEDS MORE LOVE. Seriously, it has excellent, clean art, a brilliant, tight story, and realistic characters. I love this manga. I've read it four times and it's not my favourite genre!
. Just a fun romp through the old times.
. Need to find the manga but I watched the anime. Brilliant.
On my MUST READ/WATCH list:
Tiger & Bunny
(in the middle of) Drrrrrr!
(trying to find the rest of) Monster
Puella Magi Madoka Magica
Persona (played Persona 4 and loved it. STILL need to watch the anime)
And touchmon got me hooked on no.6 with the Inukashi cosplay. I'm currently loving the manga.
That's all I can recall off the top of my head. There's probably more but I don't remember