Figured I'd revive this thread and post up mine so far (too lazy to edit out teams but it does the trick):
1 - Montreal (via EDM) - Taylor Hall, F, EDM
2 - New York - Tyler Seguin, F, BOS
3 - Toronto - Brett Connolly, F, TBL
4 - Chicago - Nino Niederreiter, F, NYI
5 - Atlanta - Alexander Burmistrov, F, ATL
6 - Calgary (from CHI via PIT) - Ryan Johansen, F, CLB
7 - Calgary - Jack Campbell, G, DAL
8 - Los Angeles - Cam Fowler, D, ANH
9 - Ottawa - Jeff Skinner, F, CAR
10 - Chicago (from CGY via CLB) - Mikael Granlund, F, MIN
11 - Phoenix - Vladimir Tarasenko, F, STL
12 - Florida - Nick Bjugstad, F, FLA
13 - Phoenix (from MTL) - Beau Bennett, F, PIT
14 - Anaheim - Evgeni Kuznetsov, F, WSH
15 - Vancouver - Jaden Schwartz, F, STL
16 - Detroit - Emerson Etem, F, ANH
17 - Montreal (from EDM) - Brandon Gormley, D, PHX
18 - New York - Austin Watson, F, NSH
19 - Detroit (from Toronto) - Kirill Kabanov, F, NYI
20 - Edmonton (from CHI via TOR) - Riley Sheahan, F, DET
21 - Vancouver (from ATL) - Erik Gudbranson, D, FLA
22 - Pittsburgh - Calle Järnkrok, F, DET
23 - Phoenix (from CGY) - Tyler Toffoli
24 - Los Angeles - Teemu Pulkkinen
25 - Ottawa - Stanislav Galiev
Only up to 25 so far, but not too bad. Will update as time goes on.