For me, there are a few factors that decide how much I like a particular Pokemon.
Design: Simply put, if I don't like how a Pokemon looks I probably won't like it, period
Offensive capabilities: A Pokemon doesn't have to possess great overall stats or be competitively viable (some of my favorite Pokemon are NU), but workable offenses are a must for me. If I like a Pokemon I want to be able to use it in-game (where decent attacking capabilities are obviously very important), and hell, even competitively I don't want Walls that are potential setup fodder. Speed is nice, but mostly I want a Pokemon that can at least hit reasonably hard.
Concept: Simply put, I will almost inevitably like Pokemon based on cats or dogs. Same goes for dinosaur Pokemon, and to a lesser degree all things high tech and futuristic. Pokemon that are surrounded in mystery also intrigue me, as well as dangerous Pokemon. I'm also biased towards legendaries, they're often the highlight on any given Pokedex and have a lot of history behind them.
Experiences with said Pokemon: If a Pokemon has helped me win many important battles, that will naturally make me think fondly of it. I generally think quite poorly of Pokemon associated with stall and annoyance, or Pokemon that are cheap and overpowered (I'm mainly thinking of ExtremeKiller Arceus here).
Typing, ability and movepool: Pokemon that have unique or unusual type combinations appeal to me (especially if the type combo is strong offensively), and I love abilities that enhance offensive capabilities (whether they increase the power, accuracy, coverage or secondary effect of offensive moves), as well as abilities that protect my Pokemon from being statused or confused. The bigger the offensive movepool the better.
Obtainability: Ideally I'd like to be able to obtain a Pokemon in-game, pre-Elite 4. It shouldn't be too rare, and it certainly shouldn't be changing location all the time. I generally dislike the idea of trade evolutions, though it's hardly a deal breaker.
What are your preferences and priorities when it comes to Pokemon?
Design partially, but mostly how much I enjoy using it. Something else that plays a part is how well the name Robby goes with it. Victreebel and Medicham were the first ever two Pokemon I named Robby and also two Pokemon I have had the most fun using, which makes them my two favorites.
Official Zangoose of the Pokemon X board+Only member of my one-man team 3DS FC: 3609-1237-6725
Well, if the design is bad enough, I will not use a certain Pokemon. Period. I've heard Quagsire and Walrein can stall pretty well, but I hate their designs so I will never use them.
Stats and movepool are also huge in my eyes. I probably wouldn't use things like Dragonite at all if not for incredible stats and moves. However, like I said before, if I don't like the design of something AT ALL, I won't use it. I don't care how good it is. *glares at Arceus*
In most cases, type hardly matters. However, believe it or not I'm a real sucker for Fire/Fighting. Just... Not 2/3 of them... Also, something like Ghost/Steel would be awesome.
I'm not easily impressed; I'm usually oblivious to whatever's in front of me.
I can't hate a pokemon with godd stats, no matter how lame his design is. I also can't hate a cool looking pokemon with terrible stats. So a perfect pokemon, for me, has good stats and design, like gengar or garchomp (which IMO have great designs and factually have nice stats).