1991 -- San Jose Sharks (frequently among the top teams in the Western Conference in the regular season in recent years, but have never appeared in the Stanley Cup finals)
1992 -- Ottawa Senators (won their first conference championship in 2006-07; no Stanley Cups)
1992 -- Tampa Bay Lightning (one Stanley Cup in 2003-04, the only season they've ever made it to the finals)
1993 -- Florida Panthers (Stanley Cup finalist in 1996, swept in four games, perennial losers most years since then)
1993 -- Anaheim Mighty Ducks (probably the most successful of the post-1990 expansion teams; Stanley Cup finalist in 2002-03, Stanley Cup champions in 2006-07)
1998 -- Nashville Predators (little or no on-ice success; regularly rumored to be moving elsewhere)
1999 -- Atlanta Thrashers (perennially one of the worst NHL teams)
2000 -- Columbus Blue Jackets (one playoff appearance; have never won a playoff game)
2000 -- Minnesota Wild (have won all of two playoff series in nine years)
That's two Stanley Cups and five appearances in the Stanley Cup finals among these nine teams by my count, which make up nearly a third of the NHL right now. I'd hardly call this an overwhelming record of success for these expansion teams.
The NHL was a blast to watch in the early 1980s, right after the merger with the WHA with the young Oilers ripping up the league. It was never as good before then and it certainly isn't anywhere near as good now.