Kate Bush, "Running Up That Hill (A Deal with God)". A different kind of dancing in this video.
Prince and the Revolution, "Raspberry Beret". I started paying less attention to Prince around this time, although in retrospect, I see this album as just another example of how many genres he felt comfortable with.
The Velvet Underground, "Foggy Notion". I can't begin to describe how wonderful it was, in 1985, to get a "new" album from my favorite, long-defunct, band. Christgau called it "A Basement Tapes for the '80s".
Suzanne Vega, "Marlene on the Wall". This was the first time Vega came to our attention. It's up to you to decide whether that was an important moment or not.
Whitney Houston, "How Will I Know". The video is a cheat: Filthy Friends doing a cover of Whitney's hit, because I was intrigued by what Corin Tucker would do with the song. I love Corin, not a fan of Whitney, but stripping the song of its hooks doesn't do it any favors, IMO. Also, the line above about Suzanne Vega kinda holds for Whitney and this song.
New Order, "The Perfect Kiss". New Order cranked out great stuff like this almost at will for a while there. I loved them. Bernard Sumner got at one reason I love them when he said, regarding this song, "I haven't a clue what this is about".
Schoolly D, "P.S.K. (What Does It Mean?)". Massively influential. It's up to you to decide whether that was an important moment or not. My vote goes for "important".
Siouxsie and The Banshees, "Cities in Dust". Back in 1977, when "Hong Kong Garden" was released, I assumed the band would be lost to history, with Siouxsie getting a footnote for her fashion sense. In fairness, I don't think I knew what post-punk was in 1977 ... I'm not sure it existed yet. Anyway, like Schoolly D, this band became very influential, and were still at it in 1985 ... hell, they were still at it in 1995.
Hüsker Dü, "I Apologize". Arguably my favorite song by my favorite hardcore punk band from my favorite of their albums. Battles it out with "Foggy Notion" and "The Perfect Kiss" for my favorite track from this list. Aw, let's face it, this is my favorite song on this list.
Bonus 1985 cut: Faith No More, "We Care a Lot":