I liked the Mario party games on DS and GBA. 

I like Mario Party 9 because it has motion controls and it's upgraded graphics.

I like the second, but it didn't seem like it would be as good when it came out, since it was practically the same as the first, in terms of mini games. Never played any after the third, besides the 8th at a friend's house. I like the DS one also.

My personal favorite was Mario Party 3, because Mario Party 3 was awesome. It's also the last one I played, and the only other one I played was Mario Party 1 and screw control stick spinning. X_X

I enjoyed the original Mario Party the best; it had all I wanted in a Mario game, plus could be good for parties. Yeah, the joystick spinning let me hand raw multiple times, but its content made up for it.

First playing through each board and collecting enough stars to unlock more things, then Bowser stealing the stars so you have to go get them... and then the star board popping out! Just amazing! And it also is home of my favorite mini-game: Running of the Bulb. One of the very few games of the Mario party series where all four people have to work together against a common enemy.

Sure, it could have used a little fine tuning; the crane game taking so many coins from someone was just a fight waiting to happen, and if a computer got hold of you as a player, you would be almost guaranteed never being able to escape. Also the game where you are in the Bowser suit and the other three people bop you, stealing 10 coins each bop was pretty unfair too. But the other Mario Party games just never excited me as much as the original.

I'm gonna be ranting about my favorite Mario Party...
No there will not be a TL;DR version. Read it or weep. =P
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So I was in Grade 1. My friend comes over one day and brings her new game over. It was Mario Party 6. I was all excited to try out this new game along with my sister and her sister. We did a Party game. We play Faire Square, 20 turns. (We unfortunately didn't finish the whole game) I had no idea what the concept of the board was, nor did I have any knowledge of the other mechanics as well. So I was pretty lost. XD
We play some mini-games at the end of every turn. (like in every other Mario Party LOL) From what I remember, we played: Ball Dozers, Crate and Peril, Daft Rafts, Granite Getaway and Control Shtick. I had a fun time playing, even if I did lose most of them. (It was my 1st time playing so uh I obviously didn't do that well XD)
So when my friend gets to that star space, she was buying multiple stars. I was like "WAIT WHAT, YOU CAN DO THAT?!?!" because no other Mario Party before it had a mechanic like that. So then when I get there, (I had 67 coins XP) I just bought as many stars as I could. Which was 3. :p
Then my friend starts using orbs and sets them on the board. I was like "Huh?" then someone landed on it and learned what the orbs did. I loved the concept it. I then get plenty of orbs and set as many as I could on the board. XD
So then when it was nighttime, I learned that there was a new mechanic: Day & Night. When it was Nighttime, Twila made each star 5 coins. I was shocked. My friend got as many stars as she could. I unfortunately could not get there within the time. :/
So then my friend had to leave... But then I was grateful for having her introduce me to this game. I had a WONDERFUL time and didn't want to stop playing it. So I was determined to get it.
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So one day, (was still in Grade 1) I couldn't go to school since I was a bit sick. It was just me and my mom. She takes me to the mall. (as I couldn't be home alone) I'm just impatient for her to get clothes and other stuff.
...But then we walk by an EB Games. I ask her if I can buy a game. We go inside, and I notice Mario Party 6 was there. I was like "OH HELL YEAH, I'M SO GETTING THIS " We finally get home, and I couldn't wait to try it on my own.
I was having the best time of my life. I played Towering Treetop. (a complete game this time ;p) I was having so much fun. When the mini-game randomizer comes up, guess what my 1st mini-game was? Daft Rafts. I was kinda confused about the mini-game rules at 1st, but then after a few practices, I do the real thing. I won. I also remember playing Cannonball Fun, Same is Lame but that's it. Don't remember the others XD
So I get the 1st star. Then the star appears at a faraway location...
So then I remember Orbs. I used my Yellow/Red orbs as soon as I possibly could since it was so fun setting them on the board. Then when my rivals paid the price I was even happier.
Night falls, and I learn you can use Pink Boo to steal. I was like "oh hey that's like Chain Chomp from Mario Party 5". So then I visit him and have him steal stars. Fortunately my rivals didn't get to him. XD
So at the end of the game, guess who won? Me. I had 6 stars and like 70+ coins. (approximate, don't remember exactly how much LOL) I was so happy I won my 1st board, so I decided to do another. Faire Square.
So I do Faire Square. I was like "Hey, I remember playing this with my friend!" I remembered the Slot Machine, the Orbs, the buying of multiple stars... I was in heaven. Oh my god it was the best time ever. When Twila made the stars 5 coins, I took advantage of that. Because of it, I had like 30+ stars. XD I won again.
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Ok, now enough about my history... xP
I love the boards of this game to death. The orbs, the Day & Night, the events, the mechanics just made this an amazing game for me to play. I love Faire Square and E. Gadd's Garage. I love the orbs on E. Gadd's Garage and the events, even if it is a simple board. And when I say orbs, I mean orbs available. (YES I'M NERDY TO THE POINT WHERE I KNOW THE ORBS AVAILABLE ON EVERY BOARD XD)
I love the mini-games of this Mario Party as well... Though I hate the luck mini-games, Stage Fright and Snow Brawl (as the lone player), Conveyor Bolt (Nighttime as the lone player) and Ray of Fright (as the team). Those mini-games I can only win if I'm lucky.
I loved this game as a kid and I still do to this day. It's my favorite of the GCN Mario Parties. Actually it's my favorite in the Mario series and one of my favorite games ever!

I voted for 3, because it was the last one I played (excluding a five minute round of a GBA version), and it seemed like an improvement on the first two to me. The boards were my favorite part about it. Although, seeing how popular 7 seems to be, It looks like I need to try it.

I honestly hate Mario Party 7 with a PASSION. Lack of mini-games, not many worthy mini-games, a HORRIBLE system on the party mode, and nerfed/badly changed Orbs from Mario Party 6. 
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The mini-games: I think they focused more on the Mic mini-games than the regular mini-games. Instead of seeing the usual 23 4 player mini-games, you see 13. I believe 5 others went to 4-player mini-games. Instead of seeing the usual 11-12 1 vs. 3 mini-games, you see 9. 5 of those are also in mic mini-games. And again, there's not many noteworthy mini-games either.
And the Bowser Mini-Games on Party Mode, guess what? This is the 1st Mario Party that can cause you to lose A STAR if you LOSE a mini-game. If you get a Single-Player one, you better pray because all of those single player Bowser games are mainly based on luck. The multiplayer ones are much less luck based, and they actually rely on skill. Also, if you're lucky, your rivals will lose whatever's at stake too.
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Oh my god, let me get into the Bowser Time. This thing, is what pretty much ruined the game for me. There's a Bowser Meter, and every turn it fills up. Every 5 turns, Bowser gets angry and it causes the most unfair events ever. He can make EVERYONE lose coins (either 10 or 20...), cause someone to lose a star and have it up for grabs for anyone to get, block a path of the board, or run his own orb shop that forces the unfortunate player to lose coins and possibly add a Koopa Kid Space from the shop event. There's also some board specific Bowser Time events, but they're all really unfair. We already face enough trouble from landing on his space, now every 5 turns? NO THANKS. Party mode is horrendous thanks to this mechanic.
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The orbs are terrible compared to the ones from Mario Party 6. It's not the same fun I experienced with Mario Party 6's Orbs. Here are examples:

Toady Orb: Oh my god what did they do with this orb. Instead of simply giving you the orb stolen from your rival, he uses it himself (if it's a yellow or red orb). If it's a blue or green orb, he just takes it and the owner of this space doesn't get it. If I want my rival to lose an Orb, I'd rather use a Mr. Blizzard Orb, which far outclasses Toady. But guess what? Toady Orbs and Mr. Blizzard Orbs are never available on the same board. You know what to do with your Orbs, not Toady.

Zap Orb: Was nerfed from losing 5 coins, to 3 coins a space passed instead. I don't think it was really overpowered to cause a nerf in this. =P
This Orb does not really give you many problems in both games, unless you're silly enough to use a (Gold) Mushroom while passing this. Then you just roll around in laughter, dying if you see that. XD

Warp Pipe Orb: Uh, what is the purpose of having a hazard that brings you back to the last space you started on? If you need to stop your opponent, Thwomp is a much better alternative as it ends their turn when they pass it.

Pink Boo Orb: Too chaotic, I preferred it being an event since you could have an item to protect yourself from Boo stealing from you. =P

Koopa Kid Orb: Great, another Koopa Kid Space added onto the board... Not annoying enough as it is. -__-

Hammer Bro Orb: This wasn't changed in terms of gameplay, but my god it takes forever for the "take 10 coins" animation to happen. Spiny Orb from Mario Party 6 was so much quicker than having to see this. =P

Snack Orb: Why was this not automatic like in Mario Party 6? You now actually have to predict when your opponent will steal a star from you with the Chain Chomp. No thanks, I'd much prefer Mario Party 6's automatic protection.

Also, as much as I love my Kamek Orbs, taking 3 character spaces is pretty overpowered IMO. :p

And don't get me started on Special Orbs (the Blue ones). Those are horribly unbalanced. So now, it actually matters which character you use. -__-
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Oh, and last thing: The Duel Space. Oh my god this change was freaking horrible. Instead of choosing what YOU want to wager, the prize you get is determined by a random roulette, so it's kind of like chance time. But guess what? There's a chance of you hitting an X, which makes you get NOTHING. However, an X never appears if the last place player wins the duel game.
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Yeah, this is my rant on my hatred for Mario Party 7. Too much too deal with, and it's so boring for me.

Well I played only Mario Party Six, Seven, Eight, and Nine, but I like Mario Party 6 because I liked the daytime and nighttime part, just like Horror Land in Mario Party 1 ( I watch youtube videos). It is so cool that the whole entire map changes and it gives something extra special in each board. For Example, in Clockwork Castle, in Daytime, you can catch DK to get a Star. But the whole scenario changes when at nighttime, DK is now Bowser and you have to run away in the opposite direction! Also, some events only occur during a certain time.

I see you only got the numbered Mario Parties and don't have the Advance or DS as well. I have Mario Party DS on my Nintendo DS (that's the only one I own at the moment), it's pretty interesting. but the Mario Party games I played is the first 5 Mario Parties, and Mario Party DS.

Mario party 3 is my all time favorite, as I played it the for the first time and I really enjoyed it because its fas and fun.

My favorite Mario Part is the first one ever made it may have left some burns on my hands and pain if course but I still enjoyed the game and its difficulty I'm quite supprised the game didn't harm me as much as the others but I still felt pain and probably was lucky.

I played every one of them from N64 to Wii, but the one I enjoyed most was Mario party 7.

I'd have to say, Mario Party 9.  I just like the inclusions of Boss Battles, like in Mario Party DS.

It's been a while since I've played any Mario Party games, but I think my favorite one was Mario Party 3. I liked the mini-games and the way the game worked, , though I can't remember everything about it, since It's been a long time since I've played it. One of the things I do remember though is the Battle Royal mode, which I liked.

I will go along with Mario Party 7 because that is the only one in the series that I played and I loved it, I remember playing with all my friends for a couple of hours per day.

My favorite Mario Party game is Mario Party 8. It is the best combination of minigames, and it gives you a lot of the best ayatems and boards. It is definitely the best party game ever made.