I think each generation has its own strengths and weaknesses. I've been playing since the early days - Pokemon Yellow was the second game I owned after Donkey Kong Country 2, so Pokemon was my initiation to gaming, and Generation I my initiation to Pokemon, so to speak. If I was to highlight certain aspects that some generations did well, and some generations did poorly, it'd be something like this:
Pokemon design: I'll say straight off the bat that I'm not going declare certain designs objectively worse. The designs are subjective and will appeal to different people in different ways. What I can say, is that I always found myself attracted designs with a few particular characteristics. The first was simplicity of design. I used to love drawing when I was younger, even if I wasn't particularly good at it, and because of this I tended to prefer simpler Pokemon designs with more rounded and egg-like bodies than the over-complicated ones. I liked Pokemon designs that instantly told you what type they were - the type chart is so complicated, with 289 different different interactions, that not being able to immediately figure out what type a Pokemon was always seemed a chore to me, and lessened the fun in battling it. I liked Pokemon designs that stuck to one or two colours - I'm not sure why this one appeals! It just seems lessy "messy" to me than some of the more polychromatic designs. I dislike baby Pokemon unless they add functionality to what they evolve into in the form of important new moves or something along those lines. I dislike "formes" - I think it weakens the identity of a Pokemon by giving it several different feels instead of one. I also dislike the over-abundance of legendaries. Admittedly, that last one isn't a reflection on design, but I think still helps categorise whether a particular generation added a good new line of Pokemon. So, that's what I find appealing in a good Pokemon design.
By and large, these traits seem to correlate with older generations. I'd guess this had something to do with hardware limits. The 60x60 sprite limitation and 4 colour (of which two had to be white and black) on the GameBoyColour meant that polychromatic, intricate designs didn't really exist. Today's 80x80 sprite size and 16 colour sprites are far less limited in what they can do, which has led to the complexity increasing. This is not to say I don't think there are good more recent designs - I wouldn't want to paint all designs from a single generation with the same brush. For example, from Generation V I'm fond of Darmanitan and Petilil, from Generation IV I like Floatzel, and from Generation III I'm partial to Breloom and Swampert. Nor does this mean I think there aren't bad designs from earlier generations. Gen I's Mr. Mime is profoundly unappealing, as a prime example! However, overall I think my like of Pokemon designs from each generation follows the trend:
II = I >> III >> V > IV
Mechanics: I think it's fairly clear that each Pokemon game has become better than the last in terms of how the actual gameplay works - we've made a huge progress from the early days. However, I also think we have to consider that Pokemon has also made extremely slow progress. While Black and White has improved on Red and Blue's foundation, given the sheer amount of time inbetween those generations, I think I'd have expected something a little more. For example, why are we still bound by grid movement, instead of having greater degrees of freedom? If the Ranger games can do it, why can't the mainline games? Why are we still using IVs and EVs as they currently are, a completely unexplained mechanic which is mostly hidden from the casual player and is instrumental in creating the divide between competitive and casual players? Why did RSE steps backwards from GSC in so many ways, in removing the day and night system, the ability to store money, and so much else? So in this context, I feel it is fair to make two separate divisions.
The first is how good each generation's mechanics was relative to its era, and the second is how good a generation's mechanics in absolute terms. In relative terms, GSC was a big step up from RBY, which RSE then squandered completely and DPPt took little further, and in many ways made worse by compounding with an inordinately slow and clunky battle system. Thankfully, BW made some much needed changes, but still lags behind what I'd have expected from the series in that time. This leaves the list looking like this:
II > I >> V >> III > IV
In absolute terms, the games pretty much go in chronological order, for obvious reasons: in terms of gameplay, the series really has been getting better and better, although I still feel there is progress to be made in several areas. The only exception for me is Gen IV. The sacrifice of speed in battles causes the games to play incredibly slowly. I can't play DPPt for any great length of time, and miss the swift and snappy gameplay almost all the other generations present. Given how battling is the absolute fundamental part of the series, it seems fair to use this as a reason to "demote" it, leaving the list looking like this:
V > III > IV > II >> I.
Region: Each game has a very different region in terms of how it plays, and I think there's quite a noticeable difference. As with design, this is a subjective measure, but I like my gameplay fast, and I like to be presented with a variety of options so I feel like I'm determining my own story (in other words, I'm a big fan of non-linearity). I also like variety - I like my worlds to have a whole host of different locales. To top it all off, more content is usually a winner.
Generation I offers a region you can move around swiftly that is also quite large. It presents the largest element of non-linearity in the whole series - after beating Brock and Misty, you can defeat the remaining gym leaders in almost any order! (I always used to leave Sabrina til last in Yellow because that Lvl. 50 Alakazam was a beast!) The one area it really falls down, however, is variety. Because of the limitations of the GameBoy, all areas are basically the same and there's no great variation in landscape.
Generation II also presents quick and easy movement, but the non-linearity has been reduced a little. There are less possible orders in which you can take in your next challenge. In addition, Generation II is quite challenged in terms of content. While I love the fact both Kanto and Johto were present, the amount of memory this required meant that Kanto feels like an abandoned wasteland and even Johto is more than a little sparse. It also suffers from a similar variety problem to Generation I, although improvements were made.
Generation III suffers from a movement problem. A larger proportion of RSE's map is sea routes than any other generation, and Surfing is also relatively slow compared to prior games. This means the latter half of RSE can drag on quite painfully simply through taking a long time to travel anywhere. In particular, making your way to both Sootopolis and the Elite Four was not really that fun. In addition, linearity has been reduced yet again. The upsides are that Generation III is quite content rich and has much, much better variation in areas visited than either of the previous generations. It's a shame it has to be marred so much by maybe the last fifth of the game.
Generation IV is good. The variety is probably the joint best in the series with Generation V, and it is content rich. The only points of criticism I have is linearity and speed. If you compare Generation I to Generation IV in terms of what you can do it any given point in the game, Generation I wins by a landslide. You also walk like an old man everywhere and Surf like a dead thing. Thankfully water routes are not as frequent as Gen III, so the Surfing is nto quite so problematic, but it is still a problem.
Generation V is much like Generation IV, but with the old problem exaggerated. BW are the most linear games in the series to date. You're effectively marched along a set path with no option, ever, to derail. I understand why this is - BW have a much more prominent story which requires events to be done in a certain order - but I was never in the Pokemon games for the story and I deeply miss the sense of exploration from the previous games.
So, in terms of regions:
I > II >> IV > V > III.
Okay, so this is a contentious one, and I'll start off hitting hard: I've never cared for story in my Pokemon games. I'm in it for the exploration and the sense of being a kid out to explore the worlds with his Pokemon, not for the "saving humanity from legendary Pokemon!" schtick the series has headed onto recently. In particular, I found the story in BW nauseating and filled with the worst parts of modern RPGs, complete with silly names (Natural Harmonia Gropius? What in earth...), silly villains, the impossibility of a 10 year old controlling a being capable shifting the continents/destroying the universe/etc. It's also become worse lately by becoming more intrusive - the aforementioned linearity of BW. The only games with satisfying stories, for me, are Gen I and Gen II. Of these two, Gen I wins out by a little, simply because Gen II's antagonists are a rather weak and insipid reflection of their Gen I counterparts. Blue is also the best Champion, in terms of climax, of the series so far. Beating him represents a culmination of your progress against him throughout the game. So, the order goes like this:
I > II >> III > IV >> V.
I don't think there's anything major left, as far as the categories I've listed goes. For me, Generation II very narrowly edges out Generation I to take the "overall best" category, followed by Generation III, then IV and V essentially equal in last place. Some may say this is nostalgia, but I hope I've described my reasoning adequately enough that you can see it isn't true. In terms of what I look for from a Pokemon game, the series really has been declining lately. Hopefully, it'll start looking up.
EDIT: And actually, thinking about it, overall I think Generation V was maybe a very slight step-up from Generation IV, so I suppose the future is at least trending in the right way.