1995 was the first year I started watching the Draft. Just some off the top of my head which occurred on the actual draft day (as opposed to the deadline):
1995: Vancouver trades for Alexander Mogilny; In return Buffalo gets Mike Peca, a prospect, and the 14th overall pick. Mogilny was only a couple years removed from a 76 goal season and he'd be reunited with Pavel Bure in Vancouver. Relatively big deal at the time, but didn't work out as well as expected.
1999: Brian Burke burned the midnight oil to secure both of the Sedins. The original top 4 of that draft was Tampa-Atlanta-Vancouver-Chicago. Burke engineered a four team trade to reshuffle the top 4 as Atlanta-Vancouver-Vancouver-Tampa.
Tampa then traded the #4 pick to the Rangers for Nik Sundstrom, Dan Cloutier, and a future 1st. The Rangers also traded up for Jamie Lundmark at #9. It's humorous now, but Calgary Sun writer Eric Francis predicted that Brendl/Lundmark would be a superior duo to the Sedins (Brendl was playing for the Calgary Hitmen and Lundmark also tore up the WHL).
2000: The Islanders trade away Roberto Luongo (I remember this one well. Back then the draft started on Saturday morning west coast time. I rolled out of bed, turned on the TV, and the first thing they showed was a graphic with the Luongo trade. At first, I didn't believe what I saw.)
2001: The Islanders trade the 2nd overall pick, Zdeno Chara, and Bill Muckalt to Ottawa for Alexei Yashin. Allegedly Boston turned down the same package for Jason Allison.
2002: Another interesting shuffle at the top of the draft. Pretty much the entire year, it was a foregone conclusion that Jay Bouwmeester was going first. Columbus made a small trade to move up from #3 to #1 to secure Rick Nash since they were worried about Philadelphia (who had secured #4) making another move to snipe him. In the end, Bouwmeester would go #3 to Florida, but only after Florida gave Atlanta a 3rd round pick to promise to take Kari Lehtonen at #2.
2003: Another small swap at the top. Florida had #1 and had Nathan Horton at the top of their list. They figured they could trade down and still get him. Eventually Pittsburgh moved up from #3, but it wasn't a huge bounty (Mikael Samuelsson and a swap of 2nd/3rd round picks). Pens took Marc-Andre Fleury.
2007: Toronto trades #13, #44, and #98 to San Jose for Vesa Toskala and Mark Bell. Sharks use those picks to move up for Logan Couture.
2010: Florida trades Nathan Horton to Boston for Dennis Wideman and #15.
2012: Pittsburgh trades Jordan Staal to Carolina for Brandon Sutter, Brian Dumoulin, and #8.
2013: Vancouver trades Cory Schneider to New Jersey for #9.
2014: Vancouver trades Ryan Kesler to Anaheim for Nick Bonino, Luca Sbisa, and #24.