How are we defining unpopular? I'll mostly go with Smogon's oh-so-viable opinions (that word gets so annoying).
I have several, with lengthy outbursts of memories attached. I now realize most are from generation 4, but there are others too.
Arbok. We watched the early seasons of the anime when it was on TV when we were little, and I just... I don't know, the way its head is so smooth and seamlessly crosses into the hood, I just love looking at it, even today! I misheard the name and thought it's called Arbo for a while, and it was, along with Abra, my favourite Pokémon when I was little. Oddly enough, after all these years, I think I've never had one.
Wurmple. I love it and all its evolutions and the way they evolve, which I unsuccessfully tried to determine experimentally by catching Wurple in the grass and in the forest before reading that it was at random. For me, Wurmple is THE early caterpillar Pokémon. It's just so cute and so familiar, always on Hoenn's early few routes which I know, like the entire region, like the back of my hand. Beautifly is so pretty and has this cool swirly proboscis, and Dustox is so endearingly weird with the six eyes.
Burmy. I absolutely love the Burmy line, ever since I first saw Burmy on Serebii's Pokédex, with what looked like leaf eyebrows and twig legs. In fourth grade, while my sister and I were saving money for our Nintendo and our Pearl version, I used to draw the Pokémon I wanted to have, and Burmy was among them from the start, always in my favourite Plant Cloak. I had wanted a male, and imagined having a Mothim on my team. And when when my sister told me that the honey tree shook while she was playing and that she caught me a Burmy, of course it turned out to be female. Oh well, you get what you get, and she was awesome. She stayed with us for a long time, got the Pokérus along with everyone else in Eterna Forest, evolved into a Plant Cloak Wormadam and reached level 30-something in active use. She had her own Ball Capsule with swirling colouful hearts and petals, which remains unchanged in the box to this very day. Later we caught more Burmy and evolved all cloaks of Wormadam and, of course, a Mothim. He and the original Wormadam live in our forset-themed box, while the other two are in the city-themed one and the desert-themed one.
Finneon. Both Finneon and Lumineon are just beautiful, my favourite fish Pokémon ever. It was also among the ones I drew, and it was predetermined that our surfer would be Finneon. Along with Infernape the starter, Staraptor the flyer and Bibarel the all-purpose obstacle remover, he ended up always staying on the team, and picked up Waterfall and Defog. And he can battle! He can take on the rival's 15 levels higher Rapidash!
Snover. The "eeyoo eeyoo" sound it makes brings back memories on its own. I used Abomasnow a lot when link battling a friend and he was fantastic.
Shieldon. Was one of the reasons we picked Pearl, and my favourite fossil, along with...
Cranidos. I will have to use one someday.
Glaceon and Leafeon. Glaceon is my favourite Eeveelution ever. Period. I got its theme deck during Christmas time long ago, and that was the first cards I got in years. Leafeon was my sister's favourite, and it has such warm brown eyes. I used him in my emulated Moon and he did very well.
Deerling. So cute, and I love the seasons gimmick, which I actually predicted before Black and White came! Sawsbuck is awesome and in fact quite strong.
Unfezant. It has slightly mismatched stats and moves, but it is sooo cool with the mask and the elegant long tail, and the female looks so sleek.
That's all I can think of now. I'll have to open the old Nintendo these days, nostalgia gets me.