In order, starting from the remakes.
FireRed/LeafGreen is hard to pick. I don't mind Pokemon from Gen 1, but I'm not overly fond of anything either. One of my favorite legendaries is Articuno, so probably that.
Heart Gold/Soul Silver, I like quite a few, but Crobat is easily my favorite.
Emerald would be Slaking. Traunt isn't much of a problem in game. It defeats things in one hit, can learn a huge amount of moves, and can easily be switched out after beating something. My only problem is getting through Slakoth. It's cute but awful.
Platinum is Crobat again. But in terms of what was introduced, Piplup for possibly being my all time favorite starter.
Black/White is Axew.
X/Y, I really liked the variety. Aegislash was fun and I like the unique ability.
Sun/Moon, I liked the design of every Tapu. I don't know what I consider a favorite for this one. Once again I like the varitey.