the 2nd round has been our albatross basically for the entire two and a half decades i've been a fan.
off the top of my head, the only really great 2nd round pick we've had is mike peca, who was a phenomenal pick in the '92 draft after we threw away our first rounder on the immortal libor polasek. i was just a kiddo but many of us on the playground were hoping to get valeri "the pocket russian rocket" bure with our late first that year. the little bure ultimately fell to the 2nd round himself, though he was gone before we got a second shot at him.
most years, we didn't even have a second rounder. so many picks traded by burke and nonis, later gillis, and more recently traded away to "fill the age gap" by benning.
but off the top of my head, second rounders that turned into nothing: leif rohlin (omg best defenseman outside the NHL111111111111), mike fountain, taylor ellington (but he kind of sort of turned into half of ehrhoff), yann sauve (hit by a car), and rick girard (but man was he awesome at the WJC).
okay now i'm actually going to look it up:
other 2nd rounders that turned into nothing-- rob woodward (zero recollection of him), rob gordon (don't remember him either), chris mcallister (ugh, so many big stiffs during the pat quinn era), ryan bonni (so many guys i don't even remember yelling at the screen about while watching the draft), konstantin koltsov (but i hear he had a nice career in europe), denis grot (zero memory), marc-andre bernier (but at least we didn't also whiff in the first round of that draft), rodin (but you're telling me there's a chance...), alexandre mallet (come on mikey, what are you, pat quinn?)
other 2nd rounders that were okay to good-- jiri slegr (huge slapshot that never hit the net, but i was excited about him; traded for a russian buddy for bure who was terrible), jassen cullimore (chris pronger's defense partner in peterborough, was never anything for us, but carved out a decent career as a big slow bottom pair guy; traded for brashear so a decent return), dave scatchard (good grindy defensive guy that we probably should have kept; traded in the felix potvin trade), harold druken (meh but at least he played; was supposed to carry our offense into the 21st century with steve kariya, haha), chubarov (we're not worthy), mason raymond (pretty much what you want out of a 2nd rounder that's not a crazy home run), and high hopes right now for thatcher demko.
years we traded away our 2nd-- 1996, 1999*, 2000, 2001, 2004, 2006, 2010, 2011, 2013, 2015
those picks were traded for, respectively-- esa tikkanen ('96), atlanta not picking brendl or either of the sedins in the '99 draft ('00), dan cloutier ('01), johan hedberg ('04), mika noronen ('06), steve bernier ('10), a 3rd and a 4th that turned into david honzik and joseph labate ('11), derek roy ('13), baertschi ('15).
* no idea what happened to the '99 pick, but it looks like it was traded to colorado, who then traded it to washington.