1999 was the closest and involved several trades and five teams. Mostly it's just difficult for things to make sense for all every teams. But just for the walk down memory lane:
Trade #1: Chicago traded #4 to Vancouver for Bryan McCabe and a future 1st rounder. Chicago won that year's lottery and moved from #8 to #4. According to Brian Burke, he was carpooling with Blackhawks GM Bob Murray at the World Championships. Murray asked if Burke would give up #3 because he wanted both Sedins in Chicago. To that point Burke tried to remain silent about his interest in the Sedins. Murray must have eventually realized that Burke couldn't be talked out of the pick so they pivoted and talked about Chicago giving up their pick to Vancouver instead. Murray probably was concerned if neither Sedin was available at #4.
Trade #2: Tampa Bay traded #1 to Vancouver for #4, #75, and #88. Lightning GM Rick Dudley kept things close to the vest to the point where Tampa's scouts weren't sure if they were picking Pavel Brendl or Daniel Sedin. After the fact, Dudley said they would have taken Brendl had they kept the pick. He was just making Burke sweat in the hopes that he'd increase his meager offer. Dudley ended up accepting because he had a separate deal in place with the Rangers who also wanted Brendl.
Trade #3: Vancouver traded #1 to Atlanta for #3 and a future 3rd rounder. Burke managed to recoup a pick by pitching Atlanta's ownership that there'd be a PR difference between selecting Patrik Stefan at #2 versus looking cool by trading up at taking him at #1.
Trade #4: Tampa Bay traded #4 to NY Rangers for Niklas Sundstrom, Dan Cloutier, and future 1st+3rd. Tampa would trade Sundstrom for Andrei Zyuzin+ a few weeks later as well.
Brian Burke didn't know it, but he could have gotten both Sedins at #3 and #4. Rangers would have ended up with Brendl at #1 and Stefan would have gone #2 to Atlanta.