Sorry I'm behind with my picks, but I'll give it a go:
West
Dallas vs. Edmonton Dallas in 5 OT games
Detroit vs. Anaheim Detorit in 6
Colorado vs. Minnesota Colorado in 5
Vancouver vs. St. Louis St. Louis in 7 (They may always self-destuct, but they usually win at least one round)
East
Ottawa vs. NY Islanders Ottawa in 6
New Jersey vs. Boston New Jersey in 7
Tampa Bay vs. Washington Washington in 6 (I think whoever I pick in this series will lose, so good for Lightning fans)
Philadelphia vs. Toronto Toronto in 7