I want to know what people think. If you want to reply below and rank them you can but the top choice only for the poll please.

My favorite is Time, Darkness, and Sky. Sky mostly because of all the extras that the first two didn't have. I make this choice based on story, soundtrack, and game play.
Next comes Super Mystery Dungeon although I still have yet to beat the final boss. Again basing this on story, soundtrack, and game play.
Third is Red Rescue Team and Blue Rescue Team. Nostalgia has a hand in this. The story was simple but good. And I loved the soundtrack. And there were many flaws in the game play that made some things ridiculous but it still is better than last place as I can still remember how it made me feel when I first played it.
Last as I believe many agree is Gates to Infinity. But my reason is a little different I think. I loved the game. The story was definitely better than Red and Blue Rescue team's. And game play in general was better. But it had it's share of weird points. And the last point is aside from the story being fairly good it felt half baked. They focused so much on the 3D aspect that several things fell behind. The quest board was practically useless. The little mini games were fun but as a whole Paradise was anything but.

So that's my ranking. Thanks for taking the time to answer.  

After playing Super Mystery Dungeon, I had to debate to myself whether I preferred that game or Sky (which had been my clear favorite before), and I finally decided that Sky's slightly better due to 2 things, longer post story, and special episodes. If that game would've had a longer post story, Super would've been my new favorite. In addition, Sky's special episodes were all extremely enjoyable, and it was awesome to be able to play as other characters in the game besides you and your partner.

gamerforlifeforever2 :
Nice. Sadly I still have not beaten Super. So I can't say in that regard but I agree with you about sky though. The special Episodes were amazing. I loved the Igglybuff one and the Grovyle ones the best.

I'm not going to lie mystery red rescue team is my favourite one. And the only pokemon mystery dungeon game to play. And also my first one ever. I'm not able to play the others not due to having their consoles sadly.  I really like red rescue team because of how it touched me in a way. That game really has a lot of feels to it. So be prepared for when you do play it.

The Star of Music : My favorite would be Super due to it pretty much telling us that all the games are connected. Also because of the ending, that ending suprised me a lot and that says something coming from a guy who has beaten every game up to that point.

I have only played Explorers of Sky and Red Rescue Team. I have to say that Explorers of Sky is my favorite. One reason is probably because it was the first Pokémon game I ever played. I also love the storyline and I actually cried when my character "died" and then my partner was really upset. Then I was jumping for joy(remember that I was a little kid when I first played this game) when Primal Dialga revived me. My only wish is that all Pokémon games could have the same level of plot and storyline as the Mystery Dungeon games. 

I played a lot of the mystery dungeon series and it's one of my favourites I love the games, with the exception of Infinity . I'd say my favourite is Time/Sky/Darkness because I liked the story way more then the others of the series and I enjoyed the soundtrack it had. And all the guild members were fun and cool characters and I loved the idea of the guild and the recruitment system was better then the last.

Since I sadly never had Sky (I loved Explorers of Time/Darkness, don't get me wrong), I'm going to have to go with Super Mystery Dungeon here.

I've already mentioned how sucked in I am to this game. This has one of the best stories in the series overall, although the final boss was a little disappointing, for very similar reasons why I feel this way towards Gates to Infinity (although definitely not in the sound department...damn!). It took so many things that were wrong with Gates to Infinity and fixed them thoroughly. With a much longer story, an actually difficult development of the dungeons, and a fun mechanic in Looplets and Emeras, this is my favorite game, at least until I play Explorers of Sky. This also has arguably the best partner in the series for me, and I know that's probably a debatable pick. Their personality is supremely likable, and probably the first to actually seem...well...childish. There are many other fun tidbits in the story and partner's full story, but I'd be spoiling major portions of the game, so I'll let people discover it on their own. Also, the addition of so many cameos from the other three games is a very nice touch, although it, at the same time, confuses things plenty. So does that mean five humans have become Pokémon for one reason or another (if you include Gengar from Rescue Team) throughout the same world's history? Seems like a fun world to live in, having a near-apocalypse every few years...

Second is Explorers of Time and Darkness. I want to say I'd like Sky better than Super Mystery Dungeon, but I'd rather not make such blind guesses, and that takes nothing away from this amazing game, especially after the first one, while good, was flawed in a few areas. Much like what Super Mystery Dungeon did with Gates to Infinity, I feel Explorers did to Rescue Team. There's a lengthy, more streamlined story, and it contains some of my favorite characters in the whole series (Wigglytuff, Grovyle, Dusknoir). The partner in this game is another very well done personality, who's very enjoyable. However, I wish the partner wasn't such a wuss at the start, at least. As someone who suffers from phobias himself, it's a little bit past suspension of disbelief with how quickly your partner gets over all of his fears. I mean, at first, your partner's too scared to even enter the guild, and next thing you know he/she is going on every dangerous expedition with you? It doesn't make sense. Other than that, the story is lengthy, and very interesting overall. I enjoyed it for what it was worth.

Much like how first and second are close for me, third and fourth are very close, but I've got to go with the game that has more of an excuse to get things wrong, Rescue Team. Let me say this right away, though...I love the entire series as a whole, and I wish I didn't even have to choose a least favorite, since all four had some enjoyable qualities to it. But I digress. Rescue Team is a standard "first attempt" game. There were a few unnecessary limits throughout the game, the story was laid out just a bit short (although the tidbit over the Ninetails curse was cool), and the ending was...eh? To be fair, at the time it was a first at the whole Mystery Dungeon story, so it felt pretty alright, considering. And the partner was...very generic, sadly. It was just your non-specific, kind of peppy partner, and I wish a little bit more was done to develop his/her personality, since most of the characters actually had notable personalities, overall, especially the likes of Team Meanies.

Gates to Infinity...oh boy. This game almost feels like a beta of Super Mystery Dungeon, and, much like betas aught to be, is inferior to it in almost every single way. I'll admit, I had a lot of fun with this story, and was even singing its praises, until the night passed and I had already beaten it. I remember even checking online to make sure it wasn't pulling an Explorers on me, and no, it wasn't. This game is insanely short for a Mystery Dungeon game, and easy at that! And its sad, too, because it has arguably one of the most fun and diverse features of a Mystery Dungeon game: Magnagates. Utilizing the 3DS camera as a "portal," you can take any round shape you find, and turn it into a Magnagate to a Mystery Dungeon that is decided upon by a number of factors of the round shape in question. Also, some of the supporting cast was rather fun to be around, particularly Emolga. However, the lack of real personality displayed by most of the characters you encounter in story makes the overall plot fall short, even if it wasn't already actually short. With only five Pokémon to choose from for you and your partner, it also made even Rescue Team look diverse in selection, and that shouldn't happen with a fully fleshed out game. And I thought the partner was generic and pretty shallow in Rescue Team, until I met Gates to Infinity's partner. Seriously, when it comes to partners, this is as bad as it gets. There isn't one really memorable thing about him/her, and it's kind of sad. The gameplay, graphics, and sound were still there, but the story and roster fell WAY off the mark.

An additional note: I'm planning to get and play the Japan-only games at some point on my Wii. They look like fun, although I've seen very little of it.

SWTerra :

 Wow... You put a lot of thought into that. Thanks for the extremely long and good response. And I agree with a lot of it.  Sky changes some things mainly just adding new features. The story is the same. Also I finally got past the final boss in PSMD. So now I don't care if others point things out but most still won't. And if only they would translate the Wii games and give them to us. I would play them in a heartbeat! Even if it was a fan translation so long as it has decent grammar. So anyway thanks for that and have fun when you get the wii ones. Seeing as I will probably never get to play them feel free to send me a pm with an overview.  I would love to know more.

The Star of Music : Thanks! And, regarding the Wii titles, I'm more also hoping that I can get anywhere just through intuition, since I definitely don't understand Japanese. I'm hoping for the best when I do get them, but man, I'm not expecting much to come out of it until a translation comes along, myself.

Then again, I've played through, and even reviewed, one Japanese-only RPG in Klonoa Heroes, and found that game to be tremendously fun, and I doubt these small Wii titles have too much overall story, so I should be fine on that note.

My favorite is now the new super mystery dungeon. I just picked it up today and tried it out and it's honestly the only one that I really liked, mainly because of the graphics and Philemon selection. Really good for the price.

The remake of pokemon mystery dungeon time/darkness did a nice touch adding the event involving Shaymin. I always wondered what happened to grovyle after he alone with dusknoir returned to the future.