My favorite minigames of each.
Mario Party 4: Treasure Trek (I think). Swimming Derby (?).. It's a swimming minigame.
Mario Party 5: Get a Rope. Leaf Leaps.
Mario Party 6: Same is Lame. Dunk Bros.
Mario Party 7: Balloon Pop.(?) It's a mic minigame. Bowser Funstacle Course.
:| My memory sucks. xD
I believe the swimming mini-game you're talking about is Mario Medley. Anyways, my favorite mini-games(I have a lot for each and I don't put mic mini-games)
Mario Party 4: Mr. Blizzard's brigade, Balloon of Doom, Blame it on the Crane, Revers-a-Bomb, Butterfly Blitz, Bowser's Bigger Blast and Trace Race.
Mario Party 5: Coney Island, Fish Upon a star, Frozen Frenzy, Dodge Bomb, Squared Away, Revolving Fire, Mario Mechs, Defuse or Lose, Astro Logical, Rain of Fire, Cage in Cookin, Mass-a-peel and Davine Climb.
Mario Party 6: Granite Getaway, Daft Rafts, Snow Brawl, Sink Or Swim, Surge or Destroy, Clean Team(if I'm cleaning), Burnstile, Stamp By Me, Wrasslin Rapids, Hyper Sniper, Dizzy Rotisserie, Tally Me Banana, Pier Factor and Dunk Bros.
Mario Party 7: Track&Yield, Take me Ohm, Flashfright, Pogo-a-Go-Go, Tile and Error, Spider Stomp, The Final Countdown, Gimme a sign, Apes of Wrath, Fish & Cheeps, Real Smoothie, Grin and Bar it, Hammer Spammer, Shock Absorbers and Funstacle Course.