Fire: Houndoom has been my favourite Fire critter since Gen II. I love its typing, its stats, its design, its movepool... well, everything about it! I always imagine it being like the Pokemon version of Cerberus, which is kinda cool!
Water: This one's really hard, as Water's easily my favourite type. There's Kingdra, Milotic, Lapras and Lanturn duking it out for the win... and I'd probably have to go with Lapras as the victor. I've used one in every game when I had the chance to, and I've never regretted it. As well as this, I still have memories of liking it in the anime as Ash's transportation. Maybe the nostalgia is a powerful factor.
Grass: This is the opposite of the one above, as I really really dislike Grass critters. The only one that comes close to getting my approval (ha!) is Cradily. It's slow and ugly and doesn't have a great moveset... but there's something strangely endearing about it. In any event, it's certainly much better than Armaldo!
Avatar: Miss Bellum from The Powerpuff Girls | Courtesy of: Harlequin
Fire - Arcanine. If I'm not using Charizard or Typhlosion then Arcanine would definitely be my next choice as a fire type because not only is it awesome looking but it's stats are pretty good too.
Water - Kingdra. It can just as or even more effective in battle then any of the starters due to it's balanced stats and it's typing that only gives it one weakness.
Grass - Breloom. I'm not a big fan of many of the grass type pokemon that aren't starters but the one that really became a favorite of mine back in 4th gen. was Breloom. Nowadays, Breloom can have the technician ability which can make it even more dangerous in battle.
I'm not a fan of starer Pokemon anyway so this is no biggy for me!
Fire - I honestly don't like many Fire types, but one I have always quite liked since its release was Pansear. That's about it though, I honestly don't like Fire types much at all. :3
Water - Now this one is a hard choice! I'll have to go with Buizel since that's my all time favourite Pokemon due to being both tough and adorable and also being a weasel; but it was a close call between a lot of Pokemon here.
Grass - Another hard choice! Tbh I adore the majority of Grass types, but I guess my favourite is Sewaddle. It's just sooooo freaking adorable <3 Plus when it evolves it has so much power and a very interesting evolution line. :3
Fire: This is the toughest for me, as there are very few Fire types I dislike. Although slightly, I'll go with Volcarona. I fellin love with it as soon as I saw it. Arcanine in a close Second, followed by Magmortar.
Water: Sharpedo. It's a shark that's a torpedo. And Dark. Octillery comes in second, followed by Quagsire.
Grass: I don't like grass-types much. I've always view them as inferior to Fire and Water, but there are a few I don't mind. So I go with Leafeon as my favorite, followed by Exeggutor and Victreebel.