The Pokemon series has evolved over the years so much that there's now roughly a million different kinds (650). Of course, while there's always discussions over which kind is stronger, which one is more useful or which one is simply better in every way, there is always the other side of the coin which pokemon is the most useless of them all is being discussed. There's plenty of reasons to choose which pokemon is the weakest - low stats, weaknesses, how common those weaknesses are and so on - so I'm going to try and make some sort of top 10 to sort them.
Keep in mind though: "Strong Pokémon. Weak Pokémon. That is only the selfish perception of people. Truly skilled trainers should try to win with their favorites." Karen, Master Dark-type Trainer and member of the Johto Elite Four.
Something of a pet peeve of mine, Ditton isn't a useless pokemon by far. It's actually rather essential if you want to get into the breeding game, since Ditto is something of the Jack Harkness of the pokemon series, being able to breed with most of the pokemon in the game, regardless of gender or type. On the other hand, the fact that it hasn't got much originality strikes me as uninspired from a battle tactics perspective. All it does is transform into the enemy pokemon, copying everything about the enemy except for the HP stat. That way you can use it to create rather powerful tanky pokemon or simply copy an enemy damage-dealer and have it have higher than usual health, but the usability of Ditto as a real pokemon are extremely limited due to how hard it is to use properly. It's a slow pokemon, making it generally go second, probably taking it on the chin before being able to transform. It's got bad defense, so it may not be able to take the hit. It simply transforms into the enemy pokemon, making you basically have an open hand about what you pokemon can do.
On the other hand, there's something to be said about in-depth the rumors about Ditto as a pokemon go - I'm especially intrigued by the fact that Ditto resulted out of failed experiments used to attempt to clone Mew, seeing as both pokemon share both their colour and their shiny palette swap.
Another pet peeve pokemon, Castform is known as being the pokemon with boobs or testicles. Its base form looks like it has balls underneath its chin. It's also known for having the gimmick of being able to transform into different forms depending on the current weather in the region visited by the player. That, combined with the fact that Ruby and Sapphire were the first games featuring weather, allowed for good advertising of the capabilities of the new GameBoy Advance handheld. Now, in terms of relative strength, Castform is not weak - it's got stats around the levels of Dragonair and Linoone. It does, however, learn some fairly powerful moves, including Weather Ball, which changes effect depending on what weather it is.
Another extremely cute pokemon, Togepi first appeared in generation II with the introduction of eggs. Its main purpose is that of just proving the existence of eggs, and for that reason, it's mainly just a gimmick pokemon with one special thing: Metronome. It's not the only pokemon who does it, but Togepi learns it the earliest and is the only attack it will know until level 33 when it learns Ancient Power. Now, I'm not bashing Togepi. It can do some great things. Unfortunately, these things will most likely be random and very weak. No use having a Togepi use a Fire Blast if its Special Attack is crap. But hey, at least it's cute.
This pokemon really grinds my gears (get it?). While not really very weak, being resistant to most types and immune against poison as all steel types generally are, this pokemon is just... not interesting. It's just a pair of gears that spins around. If they don't spin, they die. At least Magnemite is made of magnets, and magnets are automatically awesome. In addition, they only learn two moves that receive the STAB bonus (Gear Grind and Mirror Shot), and neither is particularly powerful. I suppose Klink just falls into the trap of being a boring pokemon. That may just be me though.
Cute as a button, Hoppip is another one of those pokemon who know Splash at low level. In addition, Hoppip only learns a damaging attack at level 10, enough for other pokemon to reach their final evolution. Due to its dual grass-air typing, it's vulnerable to Flying, Poison, Rock, Fire and extremely weak against ice. It does have the advantage of being immune to ground type pokemon, but most ground types also have some other type attached to them, and most likely it's going to be one you are weak to. Besides, even if you do manage to go against someone your Hoppip might be strong against, even a gentle breeze will make short work of its low HP stat.
There is a reason for which I've chosen Caterpie to the other low level bug types in the series. I believe that this one is the weakest of them all. Up until generation 4, Caterpie would only learn Tackle and String Shot. This would make him absolutely useless against mostly everything, especially ghost type. Generation IV came along and brought Bug Bite with it, a bug type move that Caterpie can actually use. I don't see what the pokemon could actually bite with, but it's pokemon, where there's a will, there's a way.
Another extremely weak pokemon, Kricketot debuted in generation IV. It has the dubious honor of being the weakest of all bug pokemon, which is saying something, considering bug pokemon are generally weak to begin with. On the other hand, both the damaging moves it learns while leveling actually get a STAB bonus, and have rather interesting effects. Struggle Bug lowers the enemy's special attack while Bug Bite eats the enemy's berry while not doing very shabby damage. Still, it just makes me imagine the poor guy as a cockroach who does nothing but struggle to get back on its feet, flailing around doing some damage and biting stuff every once in a while.
Notorious for being the weakest pokemon in the series stat-wise, Sunkern is a cute grass pokemon that resembles a seed with a leaf on its head. No arms, no legs, no real limbs, just a bulb with a happy face. Now, it would be interesting if Sunkern were introduced later on in the series, but no dice - it's been in the series ever since generation 2, and there haven't been any weaker pokemon introduced since. While weak, Sunkern isn't by any means useless. It doesn't have the afflicting capabilities of other grass pokemon, but it can learn fairly powerful moves which receive STAB bonuses rather early on, like Solar Beam or Giga Drain. Sure they're not the best moves around, but hey, beats Tackle.
Infamous for its apparent weakness, Magikarp actually has a very well thought out story in the anime, giving mythological context to the fact that they evolve into one of the cooler pokemon in the roster. We don't count the evolutions here though, and that makes Magikarp seem like an apparent bottom of the list. It would be if it weren't so cliche to have him there. Truth is, while he only knows Splash up until level 15 (which is painful to grow by switch training), the pokemon does learn some "useful" moves. Tackle, at level 15, finally gives him an outlet for its pathetic attack power, while Flail can actually reach 200 power if you somehow have Magikarp at just one hitpoint.
Introduced in the second generation with great plans, Unknown and its 28 different forms have devolved into nothing more than a gimmick with a myriad of shapes you would only catch all of if you were really intent on catching em all. It's weak, it resembles letters, it makes mysterious stuff hard to read and they can only learn Hidden Power, a move which ALL other pokemon can learn. Basically, a good idea, ultimately evolving into a waste of space.