There are quite a few Mons series out there. If I had to pick a favorite, it would be Pokémon - it's the series that first got me into gaming, and was (unfortunately) one of the first anime series I've ever seen.
My second favorite would have to be Kaijudo: Rise of the Duel Masters, for its well-rounded characters, rich mythology, and for being a rather creative reimagining of what was more or less a Yu-Gi-Oh! knock-off with Magic: The Gathering elements.
The number three spot is occupied by Beast Keeper. No, I've never actually seen the series, but can you honestly read aloud the premise while keeping a straight face? The series is about a bunch of kids who fight with monsters, that they can also merge with, and they keep their monsters inside yo-yos. I repeat, they keep their monsters inside yo-yos. Whether the series is legitimately good or not, that by itself is pretty awesome, in a "So Bad, It's Good" kind of way.