I decided to just list all of the first round upsets in the playoffs since 1994. Yes, I have a lot of time on my hands.
President's Trophy Winners losing in the 1st round are in bold.
By upsets, I just mean the lower seed won the series. In some of these cases, the team with the most points in the regular season was the lower seed due to facing a division winner.
Since 1994, in 45 of the 128 first-round series, the lower seed has won.
In 9 of the 16 playoffs, a #1 seed has lost in the first round. So 9 of 32 #1 seeds have been eliminated in round 1.
In 12 of the 16 playoffs, a #2 seed has lost in the first round. 15 of the 32 #2 seeds have been eliminated in round 1.
1994
8) SJS def 1) DET 4-3
7) VAN def 2) CAL 4-3
7) WAS def. 2) PIT 4-2
1995
8) NYR def 1) QUE 4-2
7) SJS def 2) CAL 4-3
6) VAN def 3) STL 4-3
5) NJD def 4) BOS 4-1
1996
5) STL def 4) TOR 4-2
1997
7) EDM def 2) DAL 4-3
5) NYR def 4) FLR 4-1
1998
8) OTT def 1) NJD 4-2
7) MTL def 2) PIT 4-2
7) EDM def 2) COL 4-3
6) BUF def 3) PHI 4-1
1999
8) PIT def 1) NJD 4-3
7) BUF def 2) OTT 4-0
6) BOS def 3) CAR 4-2
5) STL def 4) PHX 4-3
2000
8) SJS def 1) STL 4-3
7) PIT def 2) WAS 4-1
2001
7) TOR def 2) OTT 4-0
7) LAK def 2) DET 4-2
6) PIT def 3) WAS 4-2
5) BUF def 4) PHI 4-2
2002
8) MTL def 1) BOS 4-2
7) OTT def 2) PHI 4-1
2003
7) ANA def 2) DET 4-0
6) MIN def 3) COL 4-3
2004
7) MTL def 2) BOS 4-3
6) CAL def 3) VAN 4-3
2006
8) EDM def 1) DET 4-2
7) COL def 2) DAL 4-1
6) ANA def 3) CAL 4-3
5) SJS def 4) NAS 4-1
2007
6) NYR def 3) ATL 4-0
5) SJS def 4) NAS 4-1
2008
6) PHI def 3) WAS 4-3
6) COL def 3) MIN 4-2
5) DAL def 4) ANA 4-2
2009
8) ANA def 1) SJS 4-2
6) CAR def 3) NJD 4-3
2010
8) MTL def 1) WAS 4-3
7) PHI def 2) NJD 4-1
6) BOS def 3) BUF 4-2
5) DET def 4) PHX 4-3
And just for comparison (and to show how much better the NHL playoffs are), here are the first round upsets in the NBA over that same period (ignoring #4 vs #5):
1994:
8) Denver def 1) Seattle 3-2
1995:
6) Houston def 3) Utah 3-2
1996:
6) Atlanta def 3) Indiana 3-2
1997:
none
1998:
7) New York def 2) Miami 3-2
1999:
8) New York def 1) Miami 3-2
6) Philadelphia def 3) Orlando 3-2
2000:
none
2001:
6) Charlotte def 3) Miami 3-0
2002:
none
2003:
6) Boston def 3) Indiana 4-2
2004:
none
2005:
6) Indiana def 3) Boston 4-3
2006:
6) LAC def 3) Denver 4-1
2007:
6) New Jersey def 3) Toronto
8) Golden State def 1) Dallas
2008:
none
2009:
6) Dallas def 3) San Antonio 4-1
2010:
7) San Antonio def 2) Dallas 4-2
So, in 16 years the NHL has had 9 #8-vs-#1, 15 #7-vs-#2, and 12 #6-vs-#3 upsets.
The NBA, in 17 years, has had only 3 #8-vs-#1, 2 #7-vs-#2, and 9 #6-vs-#3 upsets.